ore: 15:00:00, Aula 1 Dip.di Matematica

Peter Littelmann: A Pieri-Chevalley formula for the $K$-theory of flag varieties

abstract: The Chow ring of the Grassmann variety $G_{d,n}$ of $d$--dimensional subspaces of ${\bf C}^n$ has a ${\bf Z}$--basis consisting of the classes defined by the cycle represented by the Schubert variety. Let ${\cal L}$ be the ample generator of Pic~$G_{d,n}$. The classical formula of Pieri expresses the product (in the Chow ring) of the class of ${\cal L}$ with the class of a Schubert variety. In the $K$--theory of the Grassmann variety, or more generally, of a generalized flag manifold, one would like to have a similar type of formula for the product of the class of an ample line bundle and the class of the structure sheaf a Schubert variety. In the talk we will present an effective version (i.e., we provide explicit filtrations) of the combinatorial Pieri-Chevalley type formula proved by Pittie and Ram, and we discuss the close connection between what is called {\it Standard monomial theory} and an effective version of the Pieri-Chevalley type formula.

ARGOMENTO: Algebra

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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