Journal Article

On Positivity in <i>T</i>-Equivariant <i>K</i>-Theory of Flag Varieties

William Graham and Shrawan Kumar

in International Mathematics Research Notices

Volume 2008, issue Published in print January 2008 | ISSN: 1073-7928
Published online January 2008 | e-ISSN: 1687-0247 | DOI: https://dx.doi.org/10.1093/imrn/rnn093
On Positivity in T-Equivariant K-Theory of Flag Varieties

More Like This

Show all results sharing these subjects:

  • Mathematics
  • Pure Mathematics

GO

Show Summary Details

Preview

We prove some general results on the T-equivariant K-theory KT(G/P) of the flag variety G/P, where G is a complex semisimple algebraic group, P is a parabolic subgroup, and T is a maximal torus contained in P. In particular, we make a conjecture about a positivity phenomenon in KT(G/P) for the product of two basis elements written in terms of the basis of KT(G/P) given by the dual of the structure sheaf (of Schubert varieties) basis. (For the full flag variety G/B, this dual basis is closely related to the basis given by Kostant–Kumar.) This conjecture is parallel to (but different from) the conjecture of Griffeth–Ram for the structure constants of the product in the structure sheaf basis. We give explicit expressions for the product in the T-equivariant K-theory of projective spaces in terms of these bases. In particular, we establish our conjecture and the conjecture of Griffeth–Ram in this case.

Journal Article.  0 words. 

Subjects: Mathematics ; Pure Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.