A diagram algebra for Soergel modules corresponding to smooth Schubert varieties
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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.References
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Additional Information
- Antonio Sartori
- Affiliation: Mathematisches Institut, Endenicher Allee 60, Universität Bonn, 53115 Bonn, Germany
- Address at time of publication: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
- Email: antonio.sartori@math.uni-freiburg.de
- Received by editor(s): October 14, 2013
- Received by editor(s) in revised form: December 4, 2013
- Published electronically: May 11, 2015
- Additional Notes: This work has been supported by the Graduiertenkolleg 1150, funded by the Deutsche Forschungsgemeinschaft.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 889-938
- MSC (2010): Primary 16W50; Secondary 13F20, 05E05, 17B10
- DOI: https://doi.org/10.1090/tran/6346
- MathSciNet review: 3430353