Gelfand-Tsetlin-patterns and lozenge tilings

03.03.2020 15:15 - 16:45

Markus Fulmek

Abstract:

In a recent paper, Lai and Rohatgi proved a "shuffling theorem" for lozenge tilings of a hexagon with “dents" (i.e., missing triangles). We shall point out that this follows immediately from the enumeration of Gelfand-Tsetlin patterns with given bottom row. (The same observation is also contained in a recent preprint of Byun).

Moreover, we shall present a "linear algebraic" proof (involving some calculations in the algebra of linear operators on a vector space of polynomials and some manipulations of determinants) of the formula for the enumeration of symmetric Gelfand-Tsetlin patterns with fixed bottom row, which was proved by Lai in the context of enumerating symmetric lozenge tilings of a “halved" hexagon with “dents".

Organiser:
Ch. Krattenthaler
Location:

TU Wien, Dissertantenraum, Freihaus, Turm A, 8. OG., Wiedner Hauptstr. 8-10, 1040 Wien