no. 6
Cominuscule points and Schubert varieties
[Points cominuscule et variétés de Schubert]
Graham, William1 ; Kreiman, Victor2
1 Department of Mathematics, University of Georgia, Boyd Graduate Studies Research Center, Athens, GA 30602, (USA)
2 Department of Mathematics, University of Wisconsin - Parkside, Kenosha, WI 53140, (USA)
Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2519-2548.

Nous définissons la notion de point cominuscule d’une variété de Schubert dans une variété de drapeaux généralisée pour un groupe semi-simple. Nous en déduisons des formules exprimant les séries de Hilbert et multiplicités des variétés de Schubert en des points cominuscules en termes de restrictions de classes de la K-théorie tore-équivariante et de la cohomologie en ces points, ce qui permet de généraliser des formules précédemment connues pour les variétés de drapeaux de type cominuscule. Nous pouvons ainsi calculer les séries de Hilbert et les multiplicités dans de nouveaux cas. Les formules pour les variétés de Schubert sont des cas particuliers de formules qui valent plus généralement en des points cominuscules généralisés de schémas munis d’actions de tores.

We introduce the notion of a cominuscule point in a Schubert variety in a generalized flag variety for a semisimple group. We derive formulas expressing the Hilbert series and multiplicity of a Schubert variety at a cominuscule point in terms of the restrictions of classes in torus-equivariant K-theory and cohomology to that point, generalizing previously known formulas for flag varieties of cominuscule type. Thus, we can calculate Hilbert series and multiplicities in cases where these were previously unknown. The formulas for Schubert varieties are special cases of more general formulas valid at generalized cominuscule points of schemes with torus actions.

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DOI : 10.5802/aif.3450
Classification : 14M15, 05E15
Keywords: flag variety, Schubert variety, cominuscule, minuscule, equivariant, K-theory
Mot clés : variété de drapeaux, variété Schubert, cominuscule, minuscule, équivariante, K-théorie
Graham, William 1 ; Kreiman, Victor 2

1 Department of Mathematics, University of Georgia, Boyd Graduate Studies Research Center, Athens, GA 30602, (USA)
2 Department of Mathematics, University of Wisconsin - Parkside, Kenosha, WI 53140, (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Graham, William; Kreiman, Victor. Cominuscule points and Schubert varieties. Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2519-2548. doi : 10.5802/aif.3450. https://aif.centre-mersenne.org/articles/10.5802/aif.3450/

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