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A commutant realization of W^(2)_n at critical level | | Thomas Creutzig
; Peng Gao
; Andrew R. Linshaw
; | | Date: |
19 Sep 2011 | | Abstract: | 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 nleq 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 imes n matrices under the
action of SL_n imes SL_n. For nleq 4 we classify the irreducible, admissible
C-modules M with finite-dimensional M_0. | | Source: | arXiv, 1109.4065 | | Services: | Forum | Review | PDF | Favorites | |
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