Equivariant K-theory of flag varieties revisited and related results

V. Uma

Colloquium Mathematicae (2013)

  • Volume: 132, Issue: 2, page 151-175
  • ISSN: 0010-1354

Abstract

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We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring K T ( G / B ) of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in K T ( G / B ) to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of K ( X ) ℚ where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of Schubert varieties in the Grothendieck ring of G/B.

How to cite

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V. Uma. "Equivariant K-theory of flag varieties revisited and related results." Colloquium Mathematicae 132.2 (2013): 151-175. <http://eudml.org/doc/286294>.

@article{V2013,
abstract = {We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring $K_\{T\}(G/B)$ of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in $K_\{T\}(G/B)$ to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of $K(X)_\{ℚ\}$ where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of Schubert varieties in the Grothendieck ring of G/B.},
author = {V. Uma},
journal = {Colloquium Mathematicae},
keywords = {equivariant K-theory; flag varieties; structure constants; wonderful compactification},
language = {eng},
number = {2},
pages = {151-175},
title = {Equivariant K-theory of flag varieties revisited and related results},
url = {http://eudml.org/doc/286294},
volume = {132},
year = {2013},
}

TY - JOUR
AU - V. Uma
TI - Equivariant K-theory of flag varieties revisited and related results
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 2
SP - 151
EP - 175
AB - We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring $K_{T}(G/B)$ of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in $K_{T}(G/B)$ to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of $K(X)_{ℚ}$ where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of Schubert varieties in the Grothendieck ring of G/B.
LA - eng
KW - equivariant K-theory; flag varieties; structure constants; wonderful compactification
UR - http://eudml.org/doc/286294
ER -

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