##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Soichi Okada

#### Graduate School of Mathematics, Nagoya University

## Symplectic Q-functions

##### Abstract:

Schur Q-functions are a family of symmetric functions introduced by Schur in his study of projective representations of symmetric groups. They are obtained by putting t = -1 in the Hall-Littlewood functions associated to the root system of type A. (Schur functions are the t = 0 specialization.) This talk concerns symplectic Q-functions, which are obtained by putting t = -1 in the Hall-Littlewood functions associated to the root system of type C. We present several Pfaffian formulas for symplectic Q-functions similar to those for Schur Q-functions and give a tableau description. Also we discuss some conjectures including the positivity conjecture of structure constants.

Host: Brendon Rhoades

### January 9, 2018

### 10:00 AM

### AP&M 6402

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