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標(biāo)題: Titlebook: Symmetric Functions 2001: Surveys of Developments and Perspectives; Proceedings of the N Sergey Fomin Conference proceedings 2002 Kluwer Ac [打印本頁(yè)]

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Symmetric Functions and the Fock Space,We review the definition, calculation and properties of the canonical bases of the Fock space representation of .$$U_q (widehat{sl}_n )$$. We emphasize the close connection with the theory of symmetric functions (plethysm, Hall-Littlewood functions, Macdonald polynomials)
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An Introduction to Birational Weyl Group Actions,A survey is given on a class of birational Weyl group actions which have been proposed by a series of works by Y. Yamada and the author. Examples of type . are discussed in detail. In particular, a proof for the Jacobi-Trudi formula for the τ-cocycle of type . is given in the framework of matrices
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Symmetric Functions 2001: Surveys of Developments and PerspectivesProceedings of the N
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The Laplacian Method,→ .. be the Laplacian, Ω. = δ.?.. ?.δ.. This survey discusses the result that ker Ω. is isomorphic to ... and to .. (.). We focus on applications of this result in instances where the complex . has a combinatorial structure. We discuss several instances in which a complete spectral resolution of the
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,Kerov’s Central Limit Theorem for the Plancherel Measure on Young Diagrams,m λ equals dim. λ/.!, where dim λ denotes the dimension of the irreducible representation of the symmetric group .$$ mathfrak{S}_n $$ indexed by λ. As . → ∞, the boundary of the (appropriately rescaled) random shape λ concentrates near a curve Ω (Logan-Shepp 1977, Vershik-Kerov 1977). In 1993, Kerov
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From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures, semisimple Lie algebra. Lecture II outlines a proof of this result; the main idea of the proof is to relate the LR-coefficients with canonical bases and total positivity. Lecture III introduces cluster algebras, a new class of commutative algebras defined in [9] in an attempt to create an algebraic
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From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures,and total positivity. Lecture III introduces cluster algebras, a new class of commutative algebras defined in [9] in an attempt to create an algebraic framework for canonical bases and total positivity
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