2013 Fiscal Year Final Research Report
Free Field Approach to Elliptic Quantum Groups : Vertex Operator and T-Q Operator
| Project/Area Number |
21540228
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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 |
Global analysis
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| Research Institution | Yamagata University (2010-2013)
Nihon University (2009) |
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Principal Investigator |
KOJIMA Takeo 山形大学, 理工学研究科, 准教授 (80307800)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 可積分系 / 相関関数 / 自由場表現 / 楕円量子群 / スピンチェイン / 開境界条件 / 積分表示 / 量子群 |
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| Research Abstract |
We study the following 2 problems.
(1) We diagonalize the Hamiltonian of spin chains associated with quantum group Uq(A_2(2)), Uq(\hat{sl}(M|N)), and elliptic quantum group Uqp(\hat{sl}_N). We study XXZ chain with a triangular boundary (Uq(\hat{sl}_2) symmetry), and derive integral representations of correlation functions (Joint work with P.Baseilhac).(2) We construct a free field realization of Uq(\hat{sl}(N|1)) for an arbitrary level k ( complex number). We constructed free field realizations of screenings and vertex operators. We introduce the elliptic super-algebra Uqp(\hat{sl}(M|N)), and give a free field realization of Uqp(\hat{sl}(N|1)) for an arbitrary level k.
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