Combinatorics Seminar: "The nilpotent variety of an asymptotic semigroup"

Abstract: The method of contractions of the coordinate rings of affine G-varieties was developed by Borho and Kraft (1979), and Popov (1985). Later, in the early 1990s, Vinberg applied Popov's technique to analyze the coordinate ring of a connected semisimple group. The resulting variety, which resembles the asymptote of a hyperbola, has the structure of a typical algebraic semigroup and was given the name "asymptotic semigroup". In this talk, we will discuss the asymptotic semigroups from the viewpoint of the Putcha-Renner theory of canonical monoids. We will show that an asymptotic semigroup's variety of nilpotent elements, first studied by Putcha, is an equidimensional variety. The Coxeter elements of the Weyl group of the semisimple group are in bijection with the irreducible components of this variety.

Host: John Shareshian