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 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

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 
@article{10_1090_S1079_6762_99_00067_0,
     author = {Pittie, Harsh and Ram, Arun},
     title = {A {Pieri-Chevalley} formula in the {K-theory} of a {\ensuremath{\mathit{G}}/\ensuremath{\mathit{B}}-bundle}},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {102--107},
     year = {1999},
     volume = {05},
     doi = {10.1090/S1079-6762-99-00067-0},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00067-0/}
}
TY  - JOUR
AU  - Pittie, Harsh
AU  - Ram, Arun
TI  - A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1999
SP  - 102
EP  - 107
VL  - 05
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00067-0/
DO  - 10.1090/S1079-6762-99-00067-0
ID  - 10_1090_S1079_6762_99_00067_0
ER  - 
%0 Journal Article
%A Pittie, Harsh
%A Ram, Arun
%T A Pieri-Chevalley formula in the K-theory of a 𝐺/𝐵-bundle
%J Electronic research announcements of the American Mathematical Society
%D 1999
%P 102-107
%V 05
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00067-0/
%R 10.1090/S1079-6762-99-00067-0
%F 10_1090_S1079_6762_99_00067_0
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

[1] Chevalley, C. Sur les décompositions cellulaires des espaces 𝐺/𝐵 1994 1 23

[2] Fulton, William, Lascoux, Alain A Pieri formula in the Grothendieck ring of a flag bundle Duke Math. J. 1994 711 729

[3] Kostant, Bertram, Kumar, Shrawan 𝑇-equivariant 𝐾-theory of generalized flag varieties J. Differential Geom. 1990 549 603

[4] Littelmann, Peter A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras Invent. Math. 1994 329 346

[5] Pittie, Harsh V. Homogeneous vector bundles on homogeneous spaces Topology 1972 199 203

[6] Steinberg, Robert On a theorem of Pittie Topology 1975 173 177

Cité par Sources :