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A scheme related to the Brauer loop model
Algebra & Discrete Mathematics| Speaker: | Brian Rothbach, UC Berkeley |
| Location: | 1147 MSB |
| Start time: | Thu, Jan 26 2006, 12:10PM |
Description
The Brauer loop model is a quantum integral stochastic process introduced by de
Gier and Nienhuis. They observed that certain entries of the Perron-Frobenius
eigenvector of this model matched degrees of the components of the upper-upper
scheme of Knutson. In order to obtain all entries of the eigenvector, Knutson
and Zinn-Justin introduced the Brauer loop scheme, which can be described as
the set of all matrices with M · M=0,
where · is a degeneration of
normal matrix multiplication. They showed that the components correspond to
states in the loop model, and the multidegrees of each component are shown
inductively to agree with a polynomial generalization of the entries of the
Perron-Frobenius eigenvector. In particular, this gives a formula for the
multidegree of the commuting variety.
This talk will assume no prior knowledge of the Brauer loop model, the
upper-upper scheme, or multidegrees, and hopefully should be accessible.