Journal of Combinatorics

Volume 9 (2018)

Number 3

PBW bases and marginally large tableaux in type $D$

Pages: 535 – 551

DOI: https://dx.doi.org/10.4310/JOC.2018.v9.n3.a6

Authors

Ben Salisbury (Department of Mathematics, Central Michigan University, Mount Pleasant, Mich., U.S.A.)

Adam Schultze (Department of Mathematics and Statistics, University at Albany, State University of New York, Albany, N.Y., U.S.A.)

Peter Tingley (Department of Mathematics and Statistics, Loyola University, Chicago, Illinois, U.S.A.)

Abstract

We give an explicit description of the unique crystal isomorphism between two realizations of $B(\infty)$ in type $D$: that using marginally large tableaux and that using PBW monomials with respect to one particularly nice reduced expression of the longest word.

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The first author was partially supported by CMU Early Career grant #C62847 and by Simons Foundation grant #429950.

The second and third authors were partially supported by NSF grant DMS-1265555.

Received 23 June 2016

Published 18 May 2018