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In [1] Bozec gave a definition of generalized quantum groups that extends the usual definition of quantum groups to finite quivers with loops at vertices, and in [3] he introduced a theory of generalized crystals for this new family of Hopf algebras. We explicitly characterize the generalized crystal B(∞) associated to a certain family of comet-shaped… (More)

A theorem due to Tokuyama expresses Schur polynomials in terms of Gelfand-Tsetlin patterns, providing a deformation of the Weyl character formula and two other classical results, Stanley's formula for the Schur q-polynomials and Gelfand's parametrization for the Schur polynomials. We generalize Tokuyama's formula to the Hall-Littlewood polynomials by… (More)

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