Lusztig-Vogan categories of equal rank 2
Abstract
Lusztig-Vogan categories are categorifications of the principal block of the Lusztig-Vogan module over the Hecke algebra, which captures information about characters of irreducible admissible representations of a real reductive group. Lusztig-Vogan categories can be constructed as module categories over Soergel bimodules. In this paper, we describe the structure of the rank 2 Lusztig-Vogan categories corresponding to equal rank real groups. More precisely, we classify indecomposable objects and describe the action of generating Soergel bimodules, recovering the W-graph of the underlying Lusztig-Vogan module. We also provide an algorithm which completes this procedure for arbitrary finite rank Lusztig-Vogan categories, including those which do not correspond to a real reductive group.
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BibTeX
@misc{dunmore2026lusztigvogan,
title = {{Lusztig-Vogan categories of equal rank 2}},
author = {Daniel Dunmore and Anna Romanov and Victor L. Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28024},
eprint = {2608.28024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28024},
}
RIS
TY - UNPB
TI - Lusztig-Vogan categories of equal rank 2
AU - Daniel Dunmore
AU - Anna Romanov
AU - Victor L. Zhang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28024
UR - https://arxiv.org/abs/2608.28024
AB - Lusztig-Vogan categories are categorifications of the principal block of the Lusztig-Vogan module over the Hecke algebra, which captures information about characters of irreducible admissible representations of a real reductive group. Lusztig-Vogan categories can be constructed as module categories over Soergel bimodules. In this paper, we describe the structure of the rank 2 Lusztig-Vogan categories corresponding to equal rank real groups. More precisely, we classify indecomposable objects and describe the action of generating Soergel bimodules, recovering the W-graph of the underlying Lusztig-Vogan module. We also provide an algorithm which completes this procedure for arbitrary finite rank Lusztig-Vogan categories, including those which do not correspond to a real reductive group.
ER -