Displaying similar documents to “Constructing canonical bases of quantized enveloping algebras.”

The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair

Welleda Baldoni, Pierluigi Möseneder Frajria (1999)

Annales de l'institut Fourier


Let G / K a noncompact symmetric space with Iwasawa decomposition K A N . The Harish-Chandra homomorphism is an explicit homomorphism between the algebra of invariant differential operators on G / K and the algebra of polynomials on A that are invariant under the Weyl group action of the pair ( G , A ) . The main result of this paper is a generalization to the quantum setting of the Harish-Chandra homomorphism in the case of G / K being an hermitian (classical) symmetric space

Composition-diamond lemma for modules

Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)

Czechoslovak Mathematical Journal


We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra s l 2 , the Verma module over a Kac-Moody algebra, the...