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Creators/Authors contains: "Shimozono, Mark"

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  1. ; ; (, Forum of Mathematics, Sigma)
    Abstract We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath MacdonaldP-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our operators arise from integral formulas for the action of the horizontal Heisenberg subalgebra in the vertex representation of the corresponding quantum toroidal algebra. 
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  2. ; ; (, Sem. Lothar. Combin.)
    Accepted Manuscript Full Text Available
  3. ; ; (, International Mathematics Research Notices)
    Abstract We study the back stable $$K$$-theory Schubert calculus of the infinite flag variety. We define back stable (double) Grothendieck polynomials and double $$K$$-Stanley functions and establish coproduct expansion formulae. Applying work of Weigandt, we extend our previous results on bumpless pipedreams from cohomology to $$K$$-theory. We study finiteness and positivity properties of the ring of back stable Grothendieck polynomials and divided difference operators in $$K$$-homology. 
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