Algebraic Analysis of Representation Theory View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2001-2004

FUNDING AMOUNT

16700000 JPY

ABSTRACT

In this project, we focused at geometric and combinatorial aspects of representation theory. Here are main achievements in these four years.1.(1)In the coarse of the study of the form factors of exactly solvable models as integrals, their integrands have a symmetry of affine quantum groups (Miwa et al.) The representation thus obtained is in fact the tensor product of integrable representations in positive level and negative level. This result will be proved by using the result by Nakajima given below. (2)Nakajima studied global bases and crystal bases of affine quantum groups. In particular, he showed the global bases with extremal weight correspond one-to-one to the irreducible representation of the general linear groups.2.Schapira constructed a canonical stack on the symplectic manifolds. It contains a parameter, and when it vanishes, the stack is equivalent to the one of modules over the ring of the functions. 3.Tanisaki achieved the one-to-one correspondence between D-modules on the quantized flag manifold and the modules over the quantum group. 4.Nakashima constructed geometric crystals associated to the Schubert cells and prove that their ultra-discretization coincide with the crystal for Demazure modules. Kashiwara and Nakashima, together with Okado, is studying the method to use another flag manifold in order to obtai the perfect crystals. More... »

URL

https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13440006

Related SciGraph Publications

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