Supercharacters, non-commuting symmetric functions and set partition combinatorics
 
 
Description:  The representation theory of the symmetric group is a fundamental model in combinatorial representation theory because of its connections to partition and tableaux combinatorics. It has become clear in recent years that the super-representation theory of the finite unitriangular group has a similarly rich combinatorial structure built on set partitions. The main purpose of this talk is to explore the connection of the supercharacter theory of the unitriangular group with set partition combinatorics. In particular, we will describe the set partition combinatorics appearing in connection to restriction, superinduction, inflation and deflation of supercharacters, and show how these can be used to obtain a relationship between the supercharacter theory of all unitriangular groups simultaneously and the combinatorial Hopf algebra of symmetric functions in non-commuting variables that mirrors the symmetric group's relationship with the Hopf algebra of symmetric functions.
Date:  2013-11-27
Start Time:   15:00
Speaker:  Carlos André (Univ. Lisboa)
Institution:  Universidade de Lisboa
Place:  Room 5.5 - DMUC
Research Groups: -Algebra and Combinatorics
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