Abstract
The representation theory of rational Cherednik algebras of type A at t = 0 gives rise, by considering supports, to a natural family of smooth Lagrangian subvarieties of the Calogero-Moser space. The goal of this article is to make precise the relationship between these Lagrangian families and Schubert cells in the adelic Grassmannian. In order to do this we show that the isomorphism, as constructed by Etingof and Ginzburg, from the spectrum of the centre of the rational Cherednik algebra to the Calogero-Moser space is compatible with the factorization property of both of these spaces. As a consequence, the space of homomorphisms between certain representations of the rational Cherednik algebra can be identified with functions on the intersection of some Schubert cells.
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Acknowledgments
The author would like to express his sincerest thanks to Iain Gordon and Victor Ginzburg for sharing their ideas and for extensive discussions. Thanks also to Catharina Stroppel, Maurizio Martino and Olaf Schnü rer for stimulating discussions. The author is grateful to the Max-Planck-Institut für Mathematik, Bonn for its hospitality during the writing of this paper. The author was supported by the EPSRC grant EP-H028153.
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Presented by: Iain Gordon
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Bellamy, G. Rational Cherednik Algebras and Schubert Cells. Algebr Represent Theor 22, 1533–1567 (2019). https://doi.org/10.1007/s10468-018-9831-3
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DOI: https://doi.org/10.1007/s10468-018-9831-3
Keywords
- Rational Cherednik algebras
- Calogero-Moser space
- Schubert calculus
- Representation theory
- Adelic Grassmanian