Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probability distributions.
Weyl, Fusion and Demazure modules for the current algebra of sl_{r+1}
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abstract
We construct a Poincare-Birkhoff-Witt type basis for the Weyl modules of the current algebra of $sl_{r+1}$. As a corollary we prove a conjecture made by Chari and Pressley on the dimension of the Weyl modules in this case. Further, we relate the Weyl modules to the fusion modules of the current algebra defined by Feigin and Loktev, and to the Demazure modules in level one representations of the corresponding affine algebra. In particular, this allows us to establish substantial cases of the conjectures of Feigin and Loktev on the structure and graded character of the fusion modules.
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Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations
Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probability distributions.