2010 Fiscal Year Final Research Report
Study on 1-dimensional sums and special polynomials in mathematical physics in terms of path models
| Project/Area Number |
19740004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
SAGAKI Daisuke University of Tsukuba, 大学院・数理物質科学研究科, 講師 (40344866)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 量子アフィン代数 / 結晶基底 / パス模型 / Kirillov-Reshetikhin加群 / Mirkovic-Vilonen多面体 |
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| Research Abstract |
In the theory of Mirkovic-Vilonen (MV for short) polytopes, we obtain the following three results.
(1) Let P and Q be MV polytopes. We have proved that the MV polytope corresponding to the tensor product of P and Q is contained in the Minkowski sum of P and Q.
(2) We have described the crystal bases of Demazure modules and opposite Demazure modules in terms of MV polytopes.
(3) We have extended the theory of MV polytopes to the case of the quantum group associated to the nontwisted affine Lie algebra of type A.
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