1993 Fiscal Year Annual Research Report

古典群、量子群、ヘッケ環の表現論と組合せ論

Research Project

Project/Area Number	05229009
Research Institution	Aoyama Gakuin University
Principal Investigator	小池和彦青山学院大学, 理工学部, 助教授 (70146306)
Co-Investigator(Kenkyū-buntansha)	田中洋平東京商船大学, 商船学部, 助教授 (00135295) 有木進東京商船大学, 商船学部, 助教授 (40212641) 寺田至東京大学, 大学院・数理科学研究所, 助教授 (70180081)
Keywords	古典群 / ヘッケ環 / 量子群 / ロビンソン-シェーンステッド対応 / 対称群 / 複素鏡映群 / ヤング図形
Research Abstract	研究の主要なテーマは古典群やその量子群及びHecke環の表現への組合せ論的手法の応用である。Hecke環の表現はそのbraid関係を通してKnotの不変量を与えることはV.Jones等によって指摘されている。有木-小池「a Hecke algebra…」では複素鏡映群(zz/rzz)〓〓nについてそのbraid関係を保つ形でHecke環に当るもの(古典型A,B型Hecke環の一般化)を定義しその既約表現を具体的に決定した。また有木は上記の環が半単純である為の必要十分条件を「On the semi simplicity…」において与え他の複素鏡映群の系列についても「Representation…」中で同様にHecke環を定義し既約表現を具体的に構成した。小池は“Poinzare…"中で上記複素鏡映群についてMurnaghan-中山type公式及び自然表現をV=〓^nとするとき、対称テンソルと交代テンソルのテンソル積S(V)【.encircledx.】∧∨の既約表現への分解を各既約表現について母関数の形で与えた。寺田は対称群やGL(n.〓)の表現論や組合せ論で種々重要な役割ヲ果すRobinson-Schensted(以下RSと略記)対応についてこのRS対応はdual pairと密接に関係していることを観察し“A Robinson…"でspinor上のdual pair(Sp(2m,〓),Sp(2n,〓))についてRS型の対応を示した。

Research Products

(10 results)

All Other

All Publications (10 results)

[Publications] 小池和彦: "Poincare series on symmetric and alternating tensors for irreducible representations of imprimitive complex reflection groups" Journal of Algebra. (to appear).
[Publications] 小池和彦: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).
[Publications] 小池和彦: "Relative invariants of the polynomial rings over the finite and tame type quivers" Proc.Symp.in Pure Math.(A.M.S). (to appear).
[Publications] 小池和彦: "On a Conjecture of Stanley on Jack Syumcetric Eunctions" Discrete.Math. 115. 211-216 (1993)
[Publications] 小池和彦: "Relative Invariants of the Polynomial rings over the type Dr quivers" Advances in Mathematics. (to appear).
[Publications] 寺田至: "A Robinson-Schensted-type correspondence for a dual pair on spinors" J.Combin.Theorg Ser.A. 63. 90-109 (1993)
[Publications] 有木進: "Representation Theorg of a Hecke algebra of G(r.p.n)" Journal of Algebra. (to appear).
[Publications] 有木進: "On the semi simplicity of the Hecke algebra of (zz/rzz)〓〓n" Journal of Algebra. (to appear).
[Publications] 有木進: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).
[Publications] 有木進: "A decomposition of the adyoint representation of U〓(sl_2)" J.Fac.Sci.Univ.of Tokyo. 40. 141-159 (1993)

1993 Fiscal Year Annual Research Report

古典群、量子群、ヘッケ環の表現論と組合せ論

Principal Investigator

小池 和彦 青山学院大学, 理工学部, 助教授 (70146306)

Research Products

[Publications] 小池 和彦: "Poincare series on symmetric and alternating tensors for irreducible representations of imprimitive complex reflection groups" Journal of Algebra. (to appear).

[Publications] 小池 和彦: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).

[Publications] 小池 和彦: "Relative invariants of the polynomial rings over the finite and tame type quivers" Proc.Symp.in Pure Math.(A.M.S). (to appear).

[Publications] 小池 和彦: "On a Conjecture of Stanley on Jack Syumcetric Eunctions" Discrete.Math. 115. 211-216 (1993)

[Publications] 小池 和彦: "Relative Invariants of the Polynomial rings over the type Dr quivers" Advances in Mathematics. (to appear).

[Publications] 寺田 至: "A Robinson-Schensted-type correspondence for a dual pair on spinors" J.Combin.Theorg Ser.A. 63. 90-109 (1993)

[Publications] 有木 進: "Representation Theorg of a Hecke algebra of G(r.p.n)" Journal of Algebra. (to appear).

[Publications] 有木 進: "On the semi simplicity of the Hecke algebra of (zz/rzz)〓〓n" Journal of Algebra. (to appear).

[Publications] 有木 進: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).

[Publications] 有木 進: "A decomposition of the adyoint representation of U〓(sl_2)" J.Fac.Sci.Univ.of Tokyo. 40. 141-159 (1993)

小池和彦青山学院大学, 理工学部, 助教授 (70146306)

[Publications] 小池和彦: "Poincare series on symmetric and alternating tensors for irreducible representations of imprimitive complex reflection groups" Journal of Algebra. (to appear).

[Publications] 小池和彦: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).

[Publications] 小池和彦: "Relative invariants of the polynomial rings over the finite and tame type quivers" Proc.Symp.in Pure Math.(A.M.S). (to appear).

[Publications] 小池和彦: "On a Conjecture of Stanley on Jack Syumcetric Eunctions" Discrete.Math. 115. 211-216 (1993)

[Publications] 小池和彦: "Relative Invariants of the Polynomial rings over the type Dr quivers" Advances in Mathematics. (to appear).

[Publications] 寺田至: "A Robinson-Schensted-type correspondence for a dual pair on spinors" J.Combin.Theorg Ser.A. 63. 90-109 (1993)

[Publications] 有木進: "Representation Theorg of a Hecke algebra of G(r.p.n)" Journal of Algebra. (to appear).

[Publications] 有木進: "On the semi simplicity of the Hecke algebra of (zz/rzz)〓〓n" Journal of Algebra. (to appear).

[Publications] 有木進: "A Hecke algebra of (zz/rzz)〓〓n and coustruction of its irreducible representations" Advances in Mathematics. (to appear).

[Publications] 有木進: "A decomposition of the adyoint representation of U〓(sl_2)" J.Fac.Sci.Univ.of Tokyo. 40. 141-159 (1993)