ISSN:
1573-0530
Keywords:
Lie superalgebra q(n)
;
Schur–Howe–Sergeev duality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m),q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension $$\tilde H$$ of the hyperoctahedral group H k. We show that the zero-weight space of a q(n)-module with highest weight λ given by a strict partition of n is an irreducible module over the finite group $$\tilde H$$ parameterized by λ. We also discuss some consequences of this Howe duality.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007668930652
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