| * Venue | Media Centre |
| * Speaker | Aritra Bhattacharya |
| * Title | Haglund's conjecture and Clebsch-Gordan rule for Macdonald polynomials |
| Affiliation | IMSc |
| Abstract | Thesis defence (hybrid): Join Zoom Meeting zoom.us/j/93280841386 Meeting ID: 932 8084 1386 Passcode: 039996 The Macdonald polynomials are a remarkable family of symmetric functions which generalises many known family of symmetric functions, such as the Schur functions and the monomial symmetric functions. In the first part of the talk we will describe a conjecture of J. Haglund which says roughly that the normalized integral form Macdonald polynomials are Schur positive. We will discuss some partial results towards this conjecture. In the second part of the talk we will describe the product rules for type SL2 Macdonald polynomials P_m P_l and E_m P_l where P_m and E_m are the symmetric and nonsymmetric Macdonald polynomials respectively. We will discuss some techniques from double affine Hecke algebra which helps us compute the product rules. This part is a joint work with Arun Ram |
| * Announcement? | None |
| * Refreshments? | None |
| * Honorarium? | None |
| Special Arrangements? | None |
| * Host name and email | Sankaran Viswanath @@ svis@imsc.res.in |