Supercharacters and Hopf Monoids (12frg166)

The "Supercharacters and Hopf Monoids" workshop will be hosted at The Banff International Research Station.

Consider matrices with n rows and n columns, with 1’s down the diagonal, 0’s under the diagonal and arbitrary entries chosen in a finite field above the diagonal. We can multiply to such matrices and get a matrix of the same kind, and for any such matrix, we can find another one such that when we multiply them, we get the identity matrix. This set of matrices form the group of n by n unipotent upper-triangular matrices. We are interested in the representation of this group, that is the way that it can transform different spaces. In general, this problem is known to be impossible to describe, so we concentrate our attention to a well-behaved family (super-representations) of representations for these groups (one for each n). This family has nice structure that we described precisely in a recent paper. rnrnThe aim of the present focus research group is to develop further this (super)theory for other kind of groups and algebraic structures. To help us in this task, we recently discovered that there are more natural algebraic tools (Hopf monoids) to describe the super-representations in many cases.rnrnrn

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).