A Pieri-Chevalley formula in the K-theory of a $G/B$-bundle
Authors:
Harsh Pittie and Arun Ram
Journal:
Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 102-107
MSC (1991):
Primary 14M15; Secondary 14C35, 19E08
DOI:
https://doi.org/10.1090/S1079-6762-99-00067-0
Published electronically:
July 14, 1999
MathSciNet review:
1701888
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Abstract: Let $G$ be a semisimple complex Lie group, $B$ a Borel subgroup, and $T\subseteq B$ a maximal torus of $G$. The projective variety $G/B$ is a generalization of the classical flag variety. The structure sheaves of the Schubert subvarieties form a basis of the K-theory $K(G/B)$ and every character of $T$ gives rise to a line bundle on $G/B$. This note gives a formula for the product of a dominant line bundle and a Schubert class in $K(G/B)$. This result generalizes a formula of Chevalley which computes an analogous product in cohomology. The new formula applies to the relative case, the K-theory of a $G/B$-bundle over a smooth base $X$, and is presented in this generality. In this setting the new formula is a generalization of recent $G=GL_n({\mathbb C})$ results of Fulton and Lascoux.
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Additional Information
Harsh Pittie
Affiliation:
Department of Mathematics, Graduate Center, City University of New York, New York, NY 10036
Arun Ram
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544
MR Author ID:
316170
Email:
rama@math.princeton.edu
Received by editor(s):
February 9, 1999
Published electronically:
July 14, 1999
Additional Notes:
Research supported in part by National Science Foundation grant DMS-9622985.
Communicated by:
Efim Zelmanov
Article copyright:
© Copyright 1999
American Mathematical Society