Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras
Abstract
We construct a uniform model for highest weight crystals and $B(\infty)$ for generalized Kac--Moody algebras using rigged configurations. We also show an explicit description of the $\ast$-involution on rigged configurations for $B(\infty)$: that the $\ast$-involution interchanges the rigging and the corigging. We do this by giving a recognition theorem for $B(\infty)$ using the $\ast$-involution. As a consequence, we also characterize $B(\lambda)$ as a subcrystal of $B(\infty)$ using the $\ast$-involution.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.07746
- arXiv:
- arXiv:1812.07746
- Bibcode:
- 2018arXiv181207746S
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory;
- 05E10;
- 17B37
- E-Print:
- 18 pages, 1 figure