비만아 부모의 돌봄 경험: q 방법론

Advances in mathematics

Proceedings of the American Mathematical Society

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Reflection Groups And Coxeter Groups

We study the category O of representations of the rational Cherednik algebra AW attached to a complex reflection group W.W e construct an exact functor, called Knizhnik-Zamolodchikov functor: O → HW -mod, where HW is the (finite) Iwahori-Hecke algebra associated to W. We prove that the Knizhnik-Zamolodchikov functor induces an equiv- alence between O/Otor, the quotient of O by the subcategory of AW -modules supported on the discriminant, and the category of finite-dimensional HW - modules. The standard AW -modules go, under this equivalence, to certain modules arising in Kazhdan-Lusztig theory of "cells", provided W is a Weyl group and the Hecke algebra HW has equal parameters. We prove that the category O is equivalent to the module category over a finite dimensional algebra, a generalized "q-Schur algebra" associated to W.

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On the category O for rational Cherednik algebras

We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call "excited Young diagrams", and the second one is written in terms of factorial Schur Q- or P-functions. As an application, we give a Giambelli-type formula for the equivariant Schubert classes. We also give combinatorial and Pfaffian formulas for the multiplicity of a singular point in a Schubert variety.

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Excited Young diagrams and equivariant Schubert calculus

K-theoretic analogues of factorial Schur P- and Q-functions

We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call ``excited Young diagrams'' and the second one is written in terms of factorial Schur $Q$- or $P$-functions. As an application, we give a Giambelli-type formula for the equivariant Schubert classes. We also give combinatorial and Pfaffian formulas for the multiplicity of a singular point in a Schubert variety.

Hiroshi Naruse

Papers

Excited Young diagrams and equivariant Schubert calculus

K-theoretic analogues of factorial Schur P- and Q-functions

Excited Young diagrams and equivariant Schubert calculus

Double Schubert polynomials for the classical groups

Degeneracy loci classes in K-theory — determinantal and Pfaffian formula