Friday, October 30, 2020
Time  Items 

All day 

1:00pm 
10/30/2020  1:00pm The spherical subalgebra of Cherednik's double affine Hecke algebra of type A has a polynomial representation in which the algebra acts on a space of symmetric Laurent polynomials by rational qdifference operators. This representation has many useful applications e.g. to the theory of Macdonald polynomials. I'll present an alternative polynomial representation of the spherical DAHA, in which the algebra acts on a space of nonsymmetric Laurent polynomials by Laurent polynomial qdifference operators. This latter representation turns out to be compatible with a natural cluster algebra structure, in such a way that the action of the modular group on DAHA is given by cluster transformations. Based on joint work in progress with Philippe di Francesco, Rinat Kedem, and Alexander Shapiro. Location: 