25 citations · 225 across the 54 of their papers we have counts for
3 papers · 2 filters
Total positivity in loop groups I: whirls and curls
Thomas Lam, Pavlo Pylyavskyy
This is the first of a series of papers where we develop a theory of total positivity for loop groups. In this paper, we completely describe the totally nonnegative part of the pol…
A non-crossing standard monomial theory
T. Kyle Petersen, Pavlo Pylyavskyy, David E Speyer
The second author has introduced non-crossing tableaux, objects whose non-nesting analogues are semi-standard Young tableaux. We relate non-crossing tableaux to Gelfand-Tsetlin pat…
Promotion and cyclic sieving via webs
T. Kyle Petersen, Pavlo Pylyavskyy, Brendon Rhoades
We show that Schützenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreove…