AbstractIn the 1980s, there was significant progress in the $L^2$-theory of polarized variations of Hodge structure on higher dimensional varieties. In particular, according to the celebrated theorem of Cattani-Kaplan-Schmid and Kashiwara-Kawai, for a polarized variation of Hodge structure on the complement of a normal crossing hypersurface in a compact Kahler manifold, the $L^2$-cohomology and...
AbstractWe introduce certain class of quadratic algebras together with commutative subalgebras generated by additive and multiplicative Dunkl elements correspondingly. We identify these subalgebras with cohomology and K-theories of type A flag varieties. We show that value of Schubert polynomials on additive Dunkl elements is a generating function for the corresponding Littlewood-Richardson coe...
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