Algebra Seminar: The anti-spherical Hecke category for Hermitian symmetric pairs

  • Date: –15:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 , Å64119 + Zoom
  • Lecturer: Maud De Visscher (University of London)
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

Maud De Visscher (University of London) holds a seminar with the title "The anti-spherical Hecke category for Hermitian symmetric pairs". Welcome to join!

Abstract: In this talk, I will discuss the representation theory of the anti-spherical Hecke categories for Hermitian symmetric pairs $(W,P)$ over a field $k$ of characteristic $p\geq 0$. Minimal coset representatives for Hermitian symmetric pairs are fully commutative elements (as defined by Stembridge) and we will see how this property implies a much simplified diagrammatic presentation for the corresponding Hecke categories.  I will explain how the representation theory can be reduced to the simply laced cases via explicit graded Morita equivalences.

In the simply laced cases, the light leaves basis elements for the Hecke categories can be described in terms of certain generalisations of oriented Temperley-Lieb algebras. It follows from this description that the graded decomposition numbers, that is the p-Kazhdan- Lusztig polynomials for Hermitian symmetric pairs, are all characteristic free.

Time permitting, I will also discuss the connection with the (extended) Khovanov arc algebras studied by J. Brundan and C. Stroppel.

This is based on joint works with C. Bowman, N. Farrell, A. Hazi, E. Norton and C. Stroppel.

 

Welcome to join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.

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