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An immanant formulation of the dual canonical basis of the quantum polynomial ring

Abstract : We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings. Our results rely upon the natural appearance in the quantum polynomial ring of Kazhdan-Lusztig polynomials, $R$-polynomials, and certain single and double parabolic generalizations of these.
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Mark Skandera, Justin Lambright. An immanant formulation of the dual canonical basis of the quantum polynomial ring. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.915-926. ⟨hal-01185395⟩

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