Modular representation theory of algebraic groups

• Project/Area Number: 19540045
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka City University
• Principal Investigator: KANEDA MASAHARU (KANEDA Masaharu) Osaka City University, 大学院・理学研究科, 教授 (60204575)
• Co-Investigator(Kenkyū-buntansha): TANISAKI Toshiyuki 大阪市立大学, 大学院・理学研究科, 教授 (70142916) ; YAGITA Nobuaki 茨城大学, 教育学部, 教授 (20130768) ; TEZUKA Michishige 琉球大学, 理学部, 教授 (20197784) ; FURUSAWA Masaaki 大阪市立大学, 大学院・理学研究科, 教授 (50294525) ; HASHIMOTO Yoshitake 東京都市大学, 知識工学部, 教授 (20271182) ; KAWATA Shigeto 大阪市立大学, 大学院・理学研究科, 准教授 (50195103) ; ASASHIBA Hideto 静岡大学, 理学部, 教授 (70175165)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 表現論 / 正標数の半単純代数群 / 1の冪根の量子群 / tilting加群 / Weyl加群 / Loewy構造 / rigidity / 群論 / Frobenius direct image / flag variety / induced modules / complete exceptional sequence / generalized flag variety / infinitesimal thickening / reductive groups / D-modules / Humphreys-Verma modules

Research Abstract

Let G be a reductive algebraic group over a field of positive characteristic, and P a parabolic subgroup of G with the respective Weyl groups W and W_P. In joint work with Ye Jiachen we have constructed a Karoubian completeexceptional sequence of coherent sheaves E_w, w/in W/W_P, on G/P in case G is of rank atmost 2,using the representation theory of G_1P, G_1 the frobenius kernel of G.

Research Products

• [Journal Article] Rigidity of tilting modules (2011)
  • Author(s): Andersen, H.H., Kaneda M.
  • Journal Title: Moscow Math.J.{＼bf 11} no.1 Pages: 1-39
  • Peer Reviewed
• [Journal Article] On central critical values of the degree four L-functions for GSp(4) : the fundamental lemma, II, (2011)
  • Author(s): Furusawa, M., Martin, K.
  • Journal Title: Amer.J.Math. 133,no.1 Pages: 197-233
  • Peer Reviewed
• [Journal Article] Rigidity of tilting modules (2011)
  • Author(s): Andersen, H.H., Kaneda M.
  • Journal Title: Moscow Math.J. Volume: 11 no.1 Pages: 1-39
  • Peer Reviewed
• [Journal Article] Motivic cohomology of quadrics and the coniveau spectral sequence (2010)
  • Author(s): Yagita, N.
  • Journal Title: J.K-Theory 6,no.33 Pages: 547-589
  • Peer Reviewed
• [Journal Article] Coniveau filtration of cohomology of gyoups (2010)
  • Author(s): Yagita, N.
  • Journal Title: Proc.Lond.Math.Soc. (3)101,no.1 Pages: 179-206
  • Peer Reviewed
• [Journal Article] The complex cobordism of BSOn (2010)
  • Author(s): Inoue, K., Yagita, N.
  • Journal Title: Kyoto J.Math. 50,no.2 Pages: 307-324
  • Peer Reviewed
• [Journal Article] Yagita, Nobuaki Chern subrings (2010)
  • Author(s): Kameko, Masaki
  • Journal Title: Proc.Amer.Math.Soc. 138,no.1 Pages: 367-373
  • Peer Reviewed
• [Journal Article] On the structure of parabolic Humphreys-Verma modules (2009)
  • Author(s): Kaneda, M.
  • Journal Title: RIMS K＼t{o}ky＼t{u}roku Bessatsu {＼bf B11} Pages: 117-123
  • Peer Reviewed
• [Journal Article] The structure of Humphreys-Verma modules for projective spaces (2009)
  • Author(s): Kaneda, M.
  • Journal Title: J.Alg.{＼bf 322} Pages: 237-244
  • Peer Reviewed
• [Journal Article] Masaki Kashiwara and representation theory (2009)
  • Author(s): Tanisaki, T.
  • Journal Title: Algebraic analysis and around, Adv.Stud.Pure Math. Math.Soc.Japan, Tokyo 54 Pages: 11-18
  • Peer Reviewed
• [Journal Article] On the continuous cohomology groups of the 2×2 special linear group over l-adic integers (2009)
  • Author(s): Tezuka, M., Yagita, N.
  • Journal Title: Ryukyu Math.J. 22 Pages: 119-170
  • Peer Reviewed
• [Journal Article] On Auslander-Reiten components and trivial source lattices for integral group rings (2009)
  • Author(s): Kawata, S.
  • Journal Title: J.Algebra 322,no.4 Pages: 1395-1405
  • Peer Reviewed
• [Journal Article] On the structure of parabolic Humphreys-Verma modules (2009)
  • Author(s): Kaneda M.
  • Journal Title: RIMS KVt {o} kyYt {u} roku Bessatsu {\bf B11} Pages: 117-123
  • Peer Reviewed
• [Journal Article] The structure of Humphreys-Verma modules for projective spaces (2009)
  • Author(s): Kaneda M.
  • Journal Title: J.Alg. Volume 322, Issue 1 Pages: 237-244
  • Peer Reviewed
• [Journal Article] On the structure of parabolic Humphreys-Verma modules (2009)
  • Author(s): Kaneda M.
  • Journal Title: RIMS K\t{o}ky\t{u}roku Bessatsu B11 Pages: 117-123
  • Peer Reviewed
• [Journal Article] The structure of Humphreys-Verma modules for projective spaces (2009)
  • Author(s): Kaneda M.
  • Journal Title: J.Alg. 322-1 Pages: 237-244
  • Peer Reviewed
• [Journal Article] Kapranov's tilting sheaf on the Grassmannian in positive characteristic (2008)
  • Author(s): Kaneda M.
  • Journal Title: Alg. Repr.Th.{＼bf 11} Pages: 347-354
  • Peer Reviewed
• [Journal Article] Chow rings of excellent quadrics (2008)
  • Author(s): Yagita, N.
  • Journal Title: J.Pure Appl. Algebra 212,no.11 Pages: 2440-2449
  • Peer Reviewed
• [Journal Article] The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups PU(p) and exceptional Lie groups (2008)
  • Author(s): Kameko, M., Yagita, N.
  • Journal Title: Trans.Amer.Math.Soc. 360,no.5 Pages: 2265-2284
  • Peer Reviewed
• [Journal Article] Domestic canonical algebras and simple Lie algebras (2008)
  • Author(s): Asashiba, H.
  • Journal Title: Math.Z. 259,no.4 Pages: 713-754
  • NAID: 120001794399
  • Peer Reviewed
• [Journal Article] Kapranov's tilting sheaf on the Grassmannian in positive characteristic (2008)
  • Author(s): Kaneda M.
  • Journal Title: Alg.Repr.Th. 11 Pages: 347-354
  • Peer Reviewed
• [Journal Article] Kapranov's tilting sheaf on the Grassmannian revisited (2008)
  • Author(s): Kaneda M., Naito S.
  • Journal Title: 第10回代数群と量子群の表現論研究集会報告集 Pages: 188-197
• [Journal Article] Kapranov's tilting sheaf on the Grassmannian in positive characteristic (2008)
  • Author(s): Kaneda M.
  • Journal Title: Alg. Repr. Th. 11 Pages: 347-354
  • Peer Reviewed
• [Journal Article] Kapranov's tilting sheaf on the Grassmannian revisited, 第10回代数群と量子群の表現論研究集会報告集 (2008)
  • Author(s): Kaneda, M., Naito, S., Sagaki, D.
  • Journal Title: 第10回代数群と量子群の表現論研究集会報告集 Pages: 188-197
• [Journal Article] The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups ${\rm PU}(p)$ and exceptional Lie groups (2008)
  • Author(s): Kameko M. and Yagita N.
  • Journal Title: Trans.Amer.Math.Soc. 360 Pages: 2265-2284
  • Peer Reviewed
• [Journal Article] Equivariant localization of $＼bar{D}$-modules on the flag variety of the symplectic group of degree 4 (2007)
  • Author(s): Kaneda M., Ye, J.
  • Journal Title: J.Alg.{＼bf 309} Pages: 236-281
  • Peer Reviewed
• [Journal Article] Stable splitting and cohomology of p-local finite groups over the extraspecial p-group of order p3 and the exponent p (2007)
  • Author(s): Yagita, N.
  • Journal Title: Proceedings of the School and Conference in Algebraic Topology Geom.Topol.Monogr. Geom.Topol.Publ., Coventry 11 Pages: 399-434
  • Peer Reviewed
• [Journal Article] Algebraic cobordisms of a Pfister quadric (2007)
  • Author(s): Vishik A.,Yagita, N.
  • Journal Title: J.Lond.Math.Soc. (2)76,no.3 Pages: 586-604
  • Peer Reviewed
• [Journal Article] The Chow ring of the moduli space of bundles on P2 with charge 1 (2007)
  • Author(s): Kamiyama, Y.,Tezuka, M.
  • Journal Title: J.Math.Kyoto Univ. 47,no.3 Pages: 565-577
  • Peer Reviewed
• [Journal Article] A short proof of Morley's theorem (2007)
  • Author(s): Hashimoto, Y.
  • Journal Title: Elem.Math. 62,no.3 Pages: 121-121
  • Peer Reviewed
• [Journal Article] Equivariant localization of $\bar {D} $-modules on the flag variety of the symplectic group of degree 4 (2007)
  • Author(s): Kaneda M., Ye, J.
  • Journal Title: J.Algebra 309 Pages: 236-281
  • Peer Reviewed
• [Journal Article] Equivariant localization of $\bar{D}$-modules on the flag variety of the symplectic group of degree 4 (2007)
  • Author(s): Kaneda M. and Ye J.
  • Journal Title: Journal of Algebra 309 Pages: 236-281
  • Peer Reviewed
• [Journal Article] Algebraic cobordisms of a Pfister quadric (2007)
  • Author(s): Vishik, A. and Yagita N.
  • Journal Title: J.Lond.Math.Soc.(2) 76 Pages: 586-604
  • Peer Reviewed
• [Presentation] Representation theory of $F_*＼cO_{G/P}$ (2011)
  • Author(s): Kaneda M.
  • Organizer: 談話会
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2011-11-18
• [Presentation] Nonstandard cohomology vanishing of line bundles on the falg variety (2011)
  • Author(s): Andersen, H.H., Kaneda M.
  • Organizer: 稚内代数群セミナー
  • Place of Presentation: 稚内北星学園大学
  • Year and Date: 2011-02-21
• [Presentation] 群環における Auslander-Reiten成分とトレース写像が分 裂する加群について (2010)
  • Author(s): 河田成人
  • Organizer: 2010年度日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Some observations on the structure of $F_*＼cO_{G/P}$ (2010)
  • Author(s): Kaneda M.
  • Organizer: 第10回名古屋国際数学コンファレンスRepresentation Theory of Algebraic Groups and Quantum Groups
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-08-06
• [Presentation] Some observations on the structure of $F_*￥mathcal{O}_{G/P}$ (2010)
  • Author(s): Kaneda M.
  • Organizer: 第10回名古屋国際数学コンファレンスRepresentation Theory of Algebraic Groups and Quantum Groups
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2010-08-06
• [Presentation] Representation theory of $F_*＼cO_{G/P}$ (2010)
  • Author(s): Kaneda M.
  • Place of Presentation: Algebra Seminar, Aarhus Universitet
  • Year and Date: 2010-03-24
• [Presentation] Representation theory of $F_*\c0_{G/P} $ (2010)
  • Author(s): Kaneda M.
  • Organizer: Algebra Seminar
  • Place of Presentation: Aarhus Universitet
  • Year and Date: 2010-03-24
• [Presentation] Representation theory of $F_^*\cO_{G/P}$ (2010)
  • Author(s): Kaneda M.
  • Organizer: Algebra Seminar
  • Place of Presentation: Aarhus Universitet Danmark
  • Year and Date: 2010-03-24
• [Presentation] Symplectic manifolds arising from quantized enveloping algebras (2010)
  • Author(s): Tanisaki, T.
  • Organizer: The 5th International Conference on Representation Theory
  • Place of Presentation: Xian, China
• [Presentation] Quadrics (2009)
  • Author(s): Kaneda M.
  • Organizer: 可換環論seminar
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2009-11-19
• [Presentation] Projective spaces (2009)
  • Author(s): Kaneda M.
  • Organizer: 可換環論seminar
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2009-11-18
• [Presentation] Representation theory of $F_*\c0_{G/P} $ (2009)
  • Author(s): Kaneda M.
  • Organizer: 談話会
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2009-11-18
• [Presentation] Representation theory of $F_^*\cO_{G/P}$ (2009)
  • Author(s): Kaneda M.
  • Organizer: 談話会
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2009-11-18
• [Presentation] 群環の自明なソースを持つ加群とAuslander-Reiten quivers (2009)
  • Author(s): 河田成人
  • Organizer: 2009年度日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] On the structure of the Frobenius direct image of the structure sheaf of G/P (2009)
  • Author(s): Kaneda M.
  • Organizer: S＼'{e}minaire de g＼'{e}om＼'{e}trie alg＼'{e}brique, IRMAR (b＼t{a}timent 22), Universit＼'{e} de Rennes 1
  • Place of Presentation: Campus de Beaulieu
  • Year and Date: 2009-05-07
• [Presentation] On the structure of the Frobenius direct image of the structure sheaf of G/P (2009)
  • Author(s): Kaneda M.
  • Organizer: S\' {e} minaire de g\' {e} om\' {e} trie alg\' {e} brique
  • Place of Presentation: IRMAR (b\t {a} timent 22), Universit\' {e} de Rennes 1, Campus de Beaulieu
  • Year and Date: 2009-05-07
• [Presentation] On the structure of the Frobenius direct image of the structure sheaf of G/P (2009)
  • Author(s): Kaneda M.
  • Organizer: S\'{e}minaire de g\'{e}om\'{e}trie alg\'{e}brique,
  • Place of Presentation: IRMAR (b\t{a}timent 22), Universit\'{e} de Rennes1, Campus de Beaulieu France
  • Year and Date: 2009-05-07
• [Presentation] Auslander-Reiten components and trivial source modules for integral group rings (2009)
  • Author(s): 河田成人
  • Organizer: 表現論セミナー
  • Place of Presentation: 信州大学
  • Year and Date: 2009-02-21
• [Presentation] On Auslander-Reiten components of type A-infinity for integral group rings (2008)
  • Author(s): Shigeto K.
  • Organizer: Algebra Seminar
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2008-12-17
• [Presentation] Representation Theory of Quadrics II (2008)
  • Author(s): Kaneda, M.
  • Organizer: Seminar talk
  • Place of Presentation: Fudan University
  • Year and Date: 2008-11-24
• [Presentation] On the Frobenius direct image of the structure sheaf of projective homogeneous varieties (2008)
  • Author(s): Kaneda M.
  • Place of Presentation: Yangzhou University
  • Year and Date: 2008-11-21
• [Presentation] Representation Theory of Quadrics I (2008)
  • Author(s): Kaneda M.
  • Place of Presentation: Tongji University
  • Year and Date: 2008-11-19
• [Presentation] Representation Theory of Quadrics I (2008)
  • Author(s): Kaneda, M.
  • Organizer: Seminar talk
  • Place of Presentation: Tongji University
  • Year and Date: 2008-11-19
• [Presentation] On the $G_1T$-structure of parabolically induced modules (2008)
  • Author(s): Kaneda M.
  • Place of Presentation: East China Normal University
  • Year and Date: 2008-11-18
• [Presentation] On the $G_1T$-structure of parabolically induced modules (2008)
  • Author(s): Kaneda, M.
  • Organizer: Seminar talk
  • Place of Presentation: East China Normal University
  • Year and Date: 2008-11-18
• [Presentation] Representation Theory of Quadrics II (2008)
  • Author(s): Kaneda M.
  • Place of Presentation: Fudan University
  • Year and Date: 2008-01-24
• [Presentation] On complete exceptional sequences of coherent sheaves on homogeneous projective varieties (2007)
  • Author(s): Kaneda, M.
  • Organizer: 表現論seminar
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2007-12-18
• [Presentation] On the structure of parabolic Humphreys-Verma modules (2007)
  • Author(s): Kaneda, M.
  • Organizer: 組合せ的表現論の拡がり
  • Place of Presentation: 数理 解析研究所
  • Year and Date: 2007-10-25
• [Presentation] On the structure of parabolic Humphreys-Verma modules (2007)
  • Author(s): Kaneda M.
  • Organizer: 組合せ的表現論の拡がり
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2007-10-25
• [Presentation] Heller lattices and Auslander-Reiten quivers for integral group rings (2007)
  • Author(s): Shigeto K.
  • Organizer: XII International Conference on Representation Theory and Algebras (第12回多元環の表現論国際会議)
  • Place of Presentation: Nicolaus Copernicus University(ニコラウス・コペルニクス大学、トルン、ポーランド)
  • Year and Date: 2007-08-23
• [Presentation] Kapranov's tilting sheaf on the Grassmannian revisited (2007)
  • Author(s): Kaneda, M.
  • Organizer: 第10回代数群と量子群の表現論研究集会
  • Place of Presentation: 上智大学軽井沢セミナーハウス
  • Year and Date: 2007-06-02
• [Presentation] Kapranov's tilting sheaf on the Grassmannian revisited (2007)
  • Author(s): Kaneda M.
  • Organizer: 第10回代数群と量子群の表現論研究集会,07/6/2, 上智大学軽井沢セミナーハウス
  • Place of Presentation: 上智大学軽井沢セミナーハウス
  • Year and Date: 2007-06-02
• [Book] D-modules, perverse sheaves, and representation theory. Translated from the 1995 Japanese edition by Takeuchi. Progress in Mathematics, 236. xii+407 Boston, MA (2008)
  • Author(s): Hotta R., Takeuchi K., Tanisaki, T.
  • Publisher: Birkhauser Boston, Inc.
• [Book] $D$-modules, perverse sheaves, and representation theory (2008)
  • Author(s): Hotta R., Takeuchi K., Tanisaki T.
  • Total Pages: 419
  • Publisher: Birkhauser