Thursday, October 26 2023

11:30 - 12:45

11:30 - 12:45

* 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 |

Done