ラグランジアン・グラスマン多様体の同変コホモロジーとQ-関数(Equivariant cohomology of the Lagrangian Grassmannian and the factorial Q-functions)
池田, 岳 ラグランジアン・グラスマン多様体の同変コホモロジーとQ-関数(Equivariant cohomology of the Lagrangian Grassmannian and the factorial Q-functions). In: 表現論シンポジウム, 2005/11/15-18.
November 2005: 表現論シンポジウム
In 1911, I. Schur introduced a remarkable family of symmetric functions called the Q-functions, which encode the irreducible characters of projective representations of the symmetric groups. The functions have been appeared in some geometric situations, as well as in some other contexts of representation theories. I will report on a result on the equivariant cohomology of the Lagrangian Grassmannian, in which the “factorial” analogues of Q-functions, introduced by Ivanov, arise quite naturally as equivariant multiplicities of the torus fixed points in the Schubert varieties.