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Quantized universal enveloping superalgebra of typeQand a super-extension of the Hecke algebra

โœ Scribed by G. I. Olshanski

Publisher
Springer
Year
1992
Tongue
English
Weight
444 KB
Volume
24
Category
Article
ISSN
0377-9017

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In this paper we construct a basis for an irreducible module of the quantized enveloping algebra \(U_{r}(g /(n))\) which is a \(q\)-analogue of the special basis of an irreducible \(G L(n)\)-module introduced by C. de Concini and D. Kazhdan (Israel J. Math. 40, 1980, 275-290). We conjecture the basi

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If แ’„ is a classical simple Lie superalgebra แ’„ / P n , the enveloping algebra ลฝ . ลฝ ลฝ .. U แ’„ is a prime ring and hence has a simple artinian ring of quotients Q U แ’„ by ลฝ ลฝ .. Goldie's Theorem. We show that if แ’„ has Type I then Q U แ’„ is a matrix ring ลฝ ลฝ .. ลฝ . over Q U แ’„ . On the other hand, if แ’„ s