2013 Fiscal Year Final Research Report
Approach to the polynomials related to representation theory from quantum integrable systems
| Project/Area Number |
23654007
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka City University (2013)
Osaka University (2011-2012) |
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Principal Investigator |
OKADO Masato 大阪市立大学, 理学(系)研究科(研究院), 教授 (70221843)
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| Co-Investigator(Renkei-kenkyūsha) |
KUNIBA Atsuo 東京大学, 総合文化研究科, 教授 (70211886)
YAMADA Yasuhiko 神戸大学, 理学研究科, 教授 (00202383)
SAKAMOTO Reiho 東京理科大学, 理学部, 助教 (30528055)
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| Research Collaborator |
SCHILLING Anne カリフォルニア大学デーヴィス校, 数学科, 教授
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| Project Period (FY) |
2011 – 2013
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| Keywords | 量子群 |
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| Research Abstract |
The study of X=M conjecture, which originates in quantum integrable systems, equating the generating functions of highest weight elements of the tensor product of KR crystals and rigged configurations has advanced about 80% to the goal for type D. Research for the exceptional case E6 was also begun. However, the study of the relation to LLT polynomial remained to be incomplete.
We also studied the relation between tetrahedron equation and quantum groups, namely, explicit formula for the solution to the 3D reflection equation, relation between matrix elements of the intertwiner of the quantum coordinate ring and PBW bases of the quantum enveloping algebra, coincidence of the 2D reduction and the intertwiner of the tensor product of q-oscillator representations of a quantum affine algebra.
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[Presentation] Kirillov-Reshetikhin tableaux2012
Author(s)
M. Okado
Organizer
The XXIX International Colloquium on Group-Theoretical Methods in Physics
Place of Presentation
Chern Institute of Mathematics, Tianjin, China
Year and Date
2012-08-24
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