A Scheme Related to the Brauer Loop Model

Abstract

We introduce the Brauer loop scheme E := {M ∈ M N (C) : M • M = 0}, where • is a certain degeneration of the ordinary matrix product. Its components of top dimension, ⌊N 2 /2⌋, correspond to involutions π ∈ S N having one or no fixed points. In the case N even, this scheme contains the upper-upper scheme from [Knutson '04] as a union of (N/2)! of its… (More)

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