Tight monomials and the monomial basis property

  • Deng B
  • Du J
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Abstract

We generalize a criterion for tight monomials of quantum enveloping algebras associated with symmetric generalized Cartan matrices and a monomial basis property of those associated with symmetric (classical) Cartan matrices to their respective symmetrizable case. We then link the two by establishing that a tight monomial is necessarily a monomial defined by a weakly distinguished word. As an application, we develop an algorithm to compute all tight monomials in the rank 2 Dynkin case. © 2010 Elsevier Inc.

Author-supplied keywords

  • Canonical basis
  • Quantum enveloping algebra
  • Ringel-Hall algebra
  • Tight monomial

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Authors

  • Bangming Deng

  • Jie Du

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