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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The quantum analog of a symmetric pair:
a construction in type $(C_{n},A_{1}\times C_{n-1})$


Authors: Welleda Baldoni and Pierluigi Möseneder Frajria
Journal: Trans. Amer. Math. Soc. 349 (1997), 3235-3276
MSC (1991): Primary 17B37
MathSciNet review: 1390033
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Abstract: Let $\mathcal {I}$ be the ideal in the enveloping algebra of $\mathfrak {sp}(n,\mathbb C)$ generated by the maximal compact subalgebra of $\mathfrak {sp}(n-1,1)$. In this paper we construct an analog of $\mathcal I$ in the quantized enveloping algebra $\mbox {$\mathfrak {U}$}$ corresponding to a type $C_{n}$ diagram at generic $q$. We find generators for $\mathcal {I}$ and explicit bases for $\mbox {$\mathfrak {U}$}/\mathcal {I}$.


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Additional Information

Welleda Baldoni
Affiliation: Dipartimento di Matematica\ Universitá di Roma-Tor Vergata I-00100 Roma, Italy
Email: Baldoni@mat.utovrm.it

Pierluigi Möseneder Frajria
Affiliation: Dipartimento di Matematica\ Universitá di Trento I-38050 Povo, TN, Italy
Email: frajria@science.unitn.it

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01759-5
PII: S 0002-9947(97)01759-5
Received by editor(s): December 15, 1995
Article copyright: © Copyright 1997 American Mathematical Society