A commutant realization of W^(2)_n at critical level
Quantum Algebra
2020-08-10 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Representation Theory
Abstract
For n\geq 2, there is a free field realization of the affine vertex superalgebra A associated to psl(n|n) at critical level inside the bc\beta\gamma system W of rank n^2. We show that the commutant C=Com(A,W) is purely bosonic and is freely generated by n+1 fields. We identify the Zhu algebra of C with the ring of invariant differential operators on the space of n\times n matrices under SL_n \times SL_n, and we classify the irreducible, admissible C-modules with finite dimensional graded pieces. For n\leq 4, C is isomorphic to the W_n^{(2)}-algebra at critical level, and we conjecture that this holds for all n.
Keywords
Cite
@article{arxiv.1109.4065,
title = {A commutant realization of W^(2)_n at critical level},
author = {Thomas Creutzig and Peng Gao and Andrew R. Linshaw},
journal= {arXiv preprint arXiv:1109.4065},
year = {2020}
}
Comments
Some corrections and expository improvements, references added, final version. arXiv admin note: text overlap with arXiv:1201.0161