On the affine Hecke category

Joint with Leo Patimo. We give a complete (and surprisingly simple) description of the affine Hecke category for SL(3) in characteristic zero. More precisely, we calculate the Kazhdan-Lusztig polynomials, give a recursive formula for the projectors defining indecomposable objects and, for each coefficient of a Kazhdan-Lusztig polynomial, we produce a set of morphisms with such a cardinality.

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p-Jones Wenzl idempotent

Joint work with Gastón Burrull and Paolo Sentinelli. . Advances in Mathematics  352 (2019) 246-264. In this paper we find the characteristic p analogue of the classical Jones-Wenzl idempotent. We hope this to be a building block for the p-canonical basis as sl_2 is a building block for the representation theory of semi-simple Lie algebras.

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Revista Héurèka

Artículo en la primera edición de la revista héurèka, dedicada a la divulgación  de la ciencia.

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Blob algebra approach to modular representation theory

Joint work with David Plaza. Proc. Lond. Math. Soc. Vol. 121 (2020) Issue3, 656-701. We conjecture (and prove the "graded degree part") an equivalence between the type A affine Hecke category in positive characteristic and a certain "blob category" that we introduce as a quotient of KLR algebras. This conjecture has been proved recently in an amazing paper by Chris Bowman, Anton Cox, Amit Hazi!! It opens lots of questions...

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