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Award ID contains: 1939600

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  1. ; (, European Journal of Combinatorics)
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  2. ; ; (, International Mathematics Research Notices)
    Abstract We prove a conjecture of Knop–Sahi on the positivity of interpolation polynomials, which is an inhomogeneous generalization of Macdonald’s conjecture for Jack polynomials. We also formulate and prove the nonsymmetric version of this conjecture, and in fact, we deduce everything from an even stronger positivity result. This last result concerns certain inhomogeneous analogues of ordinary monomials that we call bar monomials. Their positivity involves in an essential way a new partial order on compositions that we call the bar order, and a new operation that we call a glissade. 
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  3. ; ; ; ; (, Representation Theory of the American Mathematical Society)
    We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden’ invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier–Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory. 
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  4. ; ; (, Transformation Groups)
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  5. ; (, Pure and Applied Mathematics Quarterly)
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  6. ; ; (, Annales de l'Institut Fourier)
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  7. ; (, International Mathematics Research Notices)
    Abstract We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of these results, in particular to binomial formulas involving non-symmetric interpolation Macdonald polynomials. 
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