Alexei Oblomkov (UMass): Catalan combinatorics in type B

Please note this event occurred in the past.
September 16, 2026 11:10 am - 12:10 pm ET
Seminars,
Representation Theory Seminar
Alexei Oblomkov
LGRT 1621

Catalan combinatorics in type B

For a Weyl group W of rank n with the natural n-dimensional representation h, we define as dimension of the quotient

           Cat(W)=dim (C[h x h]/ (C[h x h]_+) )_{sign component}).

If W=S_n, the symmetric group, we get the usual Catalan number by a non-trivial theorem of Haiman.  For other Weyl groups, there are only conjectures, no proofs so far.  I will explain some recent progress in type B and explain open problems and suggest research projects for interested students.