## Organizer(s) | Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi | ## Archive | |

## Website | http://www.rci.rutgers.edu/~yzhuang/math/lie-quantum.html |

## Upcoming Talks

## Friday, February 24th |

## Dmitry Vaintrob, |

## "TBA" |

Time: 12:00 PM |

Location: Hill 705 |

## Friday, March 10th |

## Eveliina Peltola, |

## "TBA" |

Time: 12:00 PM |

Location: Hill 705 |

## Friday, April 7th |

## Yi Sun, |

## "TBA" |

Time: 12:00 PM |

Location: Hill 705 |

## Past Talks

## Friday, February 17th |

## Siddhartha Sahi, |

## "Schur Q-functions and the Capelli eigenvalue problem for the Lie superalgebra q(n)" |

Time: 12:00 PM |

Location: Hill 705 |

Abstract: Let V be the associative superalgebra of type Q(n). Then V carries a two sided action of the queer Lie superalgebra q(n) and hence an action of l:= q(n)× q(n). We consider a distinguished basis {D_λ} of the algebra of l-invariant polynomial super-differential operators on V, which is indexed by strict partitions of length at most n. We show that the spectrum of D_λ, on the algebra P(V) of super-polynomials on V, is given by the factorial Schur Q-function of Okounkov and Ivanov.
This generalizes a result of Nazarov. As a further application we show that the radial projections of the spherical polynomials of the symmetric pair (q(n) x q(n),q(n)) are the classical Schur Q-functions. This is joint work with Alexander Alldridge and Hadi Salmasian and available at https://arxiv.org/abs/1701.03401 |

## Friday, February 10th |

## Wilfried Schmid, |

## "B-functions and Hodge Modules" |

Time: 12:00 PM |

Location: Hill 705 |

Abstract: After describing how b-functions come up in analysis and geometry, I shall discuss a class of examples that arose in my joint work with Kari Vilonen on unitary representation of reductive groups. |

## Friday, February 3rd |

## Robert Laugwitz, |

## "The Relative Hopf and Drinfeld center of a Monoidal Category" |

Time: 12:00 PM |

Location: Hill 705 |

Abstract: The Drinfeld (or quantum) center of a monoidal category is a well-known categorical construction with applications to quantum field theory. From the point of view of representation theory, this construction gives the Drinfeld double of a Hopf algebra. Another related construction is the Heisenberg double of a Hopf algebra, giving the Weyl algebra as an example. In this talk, I will discuss how these constructions can be adapted to the setting of a monoidal category relative to a braided monoidal category. In this generality, the double bosonization of S. Majid is recovered on the algebraic level, and a purely categorical definition of a generalization of the Heisenberg double can be given, called the relative Hopf center. Further, generalizing work of V. Ostrik, a Morita dual of the relative Drinfeld center can be identified, giving a classification of categorical modules in the case of a finite tensor category. The relative Hopf center obtains a categorical action of the Drinfeld center this way, generalizing a result of J.-H. Lu. |