Abstract crystals for quantum Borcherds-Bozec algebras
Abstract
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of ${B}(\infty)$ and ${B}(\lambda)$ as its application, where ${B}(\infty)$ and ${B}(\lambda)$ are the crystals of the negative half part of the quantum Borcherds-Bozec algebra $U_q(\mathfrak g)$ and its irreducible highest weight module $V(\lambda)$, respectively.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.10985
- arXiv:
- arXiv:2010.10985
- Bibcode:
- 2020arXiv201010985F
- Keywords:
-
- Mathematics - Representation Theory;
- 17B37;
- 17B67;
- 16G20
- E-Print:
- 31 pages