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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Coalgebras over the higher rank symplectic groups


Author: Anna Maria Paolucci
Journal: Proc. Amer. Math. Soc. 122 (1994), 371-381
MSC: Primary 17B35; Secondary 16W30, 46L60
MathSciNet review: 1201298
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Abstract: In these notes we generalize the construction obtained for the deformation of the symplectic group $ \operatorname{Sp}(2)$ to the case of any N even: $ N = 2k$. We characterize the bialgebras $ {A_q}({\operatorname{Sp}}(k))$ by generators and relations. We consider the deformation of the algebra of polynomials on the group $ {\operatorname{Sp}}(k):{\operatorname{Pol}}({\operatorname{Sp}_q}(k))$ is a $ {\operatorname{Hopf}^ \ast }$-algebra and we build $ ^ \ast $-representations of it by means of a Verma module construction.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1201298-X
PII: S 0002-9939(1994)1201298-X
Article copyright: © Copyright 1994 American Mathematical Society