Geodesic
A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle
Pittie, Harsh1 ; Ram, Arun2
1 Department of Mathematics, Graduate Center, City University of New York, New York, NY 10036
2 Department of Mathematics, Princeton University, Princeton, NJ 08544
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 102-107.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-99-00067-0

Pittie, Harsh 1 ; Ram, Arun 2

1 Department of Mathematics, Graduate Center, City University of New York, New York, NY 10036
2 Department of Mathematics, Princeton University, Princeton, NJ 08544 
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Pittie, Harsh; Ram, Arun. A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 102-107. doi : 10.1090/S1079-6762-99-00067-0. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00067-0/

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