A diagram algebra for Soergel modules corresponding to smooth Schubert varieties

Sartori, Antonio

doi:10.1090/tran/6346

A diagram algebra for Soergel modules corresponding to smooth Schubert varieties
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Trans. Amer. Math. Soc. 368 (2016), 889-938 Request permission

Abstract:

Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module categories are equivalent to the subquotient categories of the BGG category $\mathcal {O}(\mathfrak {gl}_n)$ which show up in categorification of $\mathfrak {gl}(1|1)$–representations. We construct diagrammatically the graded cellular structure and the properly stratified structure of these algebras.

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