منابع مشابه
Toric Degenerations of Bott-samelson Varieties
We study Bott-Samelson varieties for the group GLn(C), their toric degenerations and standard monomial type bases for their homogeneous coordinate rings. A 3-dimensional example is described in detail.
متن کاملSchubert Polynomials and Bott-Samelson Varieties
Schubert polynomials generalize Schur polynomials, but it is not clear how to generalize several classical formulas: the Weyl character formula, the Demazure character formula, and the generating series of semistandard tableaux. We produce these missing formulas and obtain several surprising expressions for Schubert polynomials. The above results arise naturally from a new geometric model of Sc...
متن کاملBott-Samelson Varieties and Configuration Spaces
The Bott-Samelson varieties Z are a powerful tool in the representation theory and geometry of a reductive group G. We give a new construction of Z as the closure of a B-orbit in a product of flag varieties (G/B). This also gives an embedding of the projective coordinate ring of the variety into the function ring of a Borel subgroup: C[Z] ⊂ C[B]. In the case of the general linear group G = GL(n...
متن کاملThe T–equivariant Cohomology of Bott–samelson Varieties
We consider the T–equivariant cohomology of Bott–Samelson desingularisations of Schubert varieties in the flag manifold of a connected semi–simple complex algebraic group of adjoint type with maximal torus T . We construct a combinatorially pure (in the sense of T. Braden and R. Macpherson) sheaf on the Bruhat graph of the associated Weyl group such that its global sections give the T–equivaria...
متن کاملBott-Samelson Varieties, Subword Complexes and Brick Polytopes
Bott-Samelson varieties factor the flag variety G/B into a product of CP’s with a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to tran...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2019
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-018-09852-6