2013 Fiscal Year Final Research Report
Representation theoretical aproach to multi-variate elliptic hypergeometric functions
| Project/Area Number |
22540022
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
KONNO Hitoshi 広島大学, 理学(系)研究科(研究院), 准教授 (00291477)
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| Co-Investigator(Renkei-kenkyūsha) |
JIMBO Michio 立教大学, 理学部, 教授 (80109082)
NOUMI Masatoshi 神戸大学, 自然科学研究科, 教授 (80164672)
NAKAYASHIKI Atsushi 九州大学, 数理学研究院, 准教授 (10237456)
OSHIMA Kazuyuki 愛知工業大学, 基礎教育センター, 准教授 (30547980)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 楕円量子群 / 楕円超幾何関数 / アフィン リー環 / 楕円関数 / 量子群 / 超幾何関数 / Sklyanin代数 / 可解格子模型 |
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| Research Abstract |
We have reformulated the two elliptic algebras U_{q,p}(g) and E_{q,p}(g) as topological algebras over the ring of formal power series in p and shown that they are isomorphic for g=gl_n. We also have formulated the dynamical quantum Z-algebras associated with U_{q,p}(g), and shown that the irreducibility of the U_{q,p}(g)-modules is governed by the corresponding Z-modules. As for the multivariate elliptic hypergeometric functions, we have shown that the sl_n type found by Kajihara-Noumi and Rosengren is given by a certain tensor product of the symmetric fusions of the sl_n type vertex-face intertwining vectors and their duals. Furthermore, as an application of the representations of U_{q,p}(sl_2), we have derived and analyzed the structure factor of the massless XXZ model exactly.
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