| * Venue | Media Centre |
| * Speaker | Aritra Bhattacharya |
| * Title | The Clebsch-Gordan rule for Macdonald polynomials |
| Affiliation | IMSc |
| Abstract | The type SL2 bosonic/symmetric Macdonald polynomials P_m are special cases of Askey-Wilson polynomials, also known by the names q-ultraspherical polynomials, Rogers polynomials. These polynomials are two parameter q,t-generalization of characters of SL2 representations. The electronic/nonsymmetric Macdonald polynomials E_m are closely related to the symmetric polynomials. In this talk we discuss the product rules for computing E_k*P_m and P_k*P_m. Following ideas of Martha Yip, we use techniques from double affine Hecke algebra, but execute a compression to reduce the sum from 2*3^{m-1} signed terms to 2m positive terms. We obtain two universal formulas inside the double affine Hecke algebra that capture the product E_k*P_m and P_k*P_m for all m simultaneously. This is based on joint work with Arun Ram. |
| * Announcement? | None |
| * Refreshments? | None |
| * Honorarium? | None |
| Special Arrangements? | None |
| * Host name and email | Sankaran Viswanath @@ svis@imsc.res.in |