String bases for quantum groups of type ᵣ

  title={String bases for quantum groups of type ᵣ},
  author={Arkady Berenstein and Andrei Zelevinsky},
This is the quantum deformation (or q−deformation) of the algebra of polynomial functions on the group Nr+1 of upper unitriangular (r + 1) × (r + 1) matrices. In this paper we introduce and study a class of bases in Ar which we call string bases. The main example of a string basis is given as follows. Let U+ = U+,r be the quantized universal enveloping algebra of the Lie algebra nr+1 of Nr+1 (see e.g., [10]). Then Ar is seen to be the graded dual of U+, and the basis in Ar dual to the Lusztig’s… 

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