A commutant realization of W^(2)_n at critical level

Details A commutant realization of W^(2)_n at critical level A commutant realization of W^(2)_n at critical level

2011-09-19

arxiv.org/abs/1109.4065v2

Mathematics

Quantum Algebra

Minor corrections, references added

Scientific paper

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 has a minimal strong generating set consisting of n+1 elements. For n\leq 4, C is a central quotient of the W^(2)_n-algebra at critical level, and we conjecture that this holds for all n. We identify the Zhu algebra of C with the ring of invariant differential operators on the space of n \times n matrices under the action of SL_n \times SL_n. For n\leq 4 we classify the irreducible, admissible C-modules M with finite-dimensional M_0.

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