An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic sl3 Webs

Authors

Heather M. Russell, University of RichmondFollow

Abstract

The sl₃ spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl₃). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and joins of webs. We build on Tymoczko’s bijection to give a simple and explicit algorithm for constructing all non-elliptic sl₃ webs.

Document Type

Post-print Article

Publication Date

2013

Publisher Statement

Copyright © 2013 Springer US.

The definitive version is available at: http://link.springer.com/article/10.1007/s10801-013-0428-y

DOI: 10.1007/s10801-013-0428-y

Full Citation:

Russell, Heather M. "An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic Sl3 Webs." Journal of Algebraic Combinatorics 38, no. 4 (2013): 851-62. doi:10.1007/s10801-013-0428-y.

Recommended Citation

Russell, Heather M., "An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic sl3 Webs" (2013). Department of Math & Statistics Faculty Publications. 127.
https://scholarship.richmond.edu/mathcs-faculty-publications/127