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Identities from representation theory (Q2312792)

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Language	Label	Description	Also known as
English	Identities from representation theory	scientific article

Statements

scholarly article

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Identities from representation theory (English)

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Travis Scrimshaw

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Discrete Mathematics

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publication date

18 July 2019

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full work available at URL

https://arxiv.org/abs/1805.00113

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zbMATH Keywords

Jacobi-Trudi formula

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Catalan number

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\(q\)-analog

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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q-Catalan Identities

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Counting Arrangements of 1's and -1's

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Steep polyominoes, \(q\)-Motzkin numbers and \(q\)-Bessel functions

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Construction of Sp-modules by tableaux

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Catalan, Motzkin, and Riordan numbers

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Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths

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Discrete analogues of Macdonald-Mehta integrals

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Two element lattice permutation numbers and their \(q\)-generalization

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Symplectic standard tableaux

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Some identities on the Catalan, Motzkin and Schröder numbers

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Restricted plane tree representations of four Motzkin-Catalan equations

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The Hodge theory of Soergel bimodules.

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Kirillov-Reshetikhin crystals for nonexceptional types

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Lattice path proofs for determinantal formulas for symplectic and orthogonal characters

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q-Catalan numbers

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A positivity result in the theory of Macdonald polynomials

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A proof of the \(q,t\)-Catalan positivity conjecture

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A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion

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Binomial determinants, paths, and hook length formulae

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A proof of the Bender-Knuth conjecture

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Random walks in Weyl chambers and the decomposition of tensor powers

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Crystalizing the q-analogue of universal enveloping algebras

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On crystal bases of the \(q\)-analogue of universal enveloping algebras

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Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras

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A NOTE ON RANDOM MATRIX INTEGRALS, MOMENT IDENTITIES, AND CATALAN NUMBERS

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Dominant maximal weights of highest weight modules and Young tableaux

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Branching rules for classical Lie groups using tensor and spinor methods

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Standard Young tableaux and weight multiplicities of the classical Lie groups

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Construction of orthogonal group modules using tableaux

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Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)

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Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank

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Advanced determinant calculus

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Determinants of (generalised) Catalan numbers

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On the combinatorics of crystal graphs. I: Lusztig's involution

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On the Vector Representations of Induced Matroids

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A determinant property of Catalan numbers

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On Some Alternative Characterizations of Riordan Arrays

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Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products

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Kostka polynomials and energy functions in solvable lattice models

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On the generating functions for certain classes of plane partitions

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Existence of Kirillov–Reshetikhin crystals for nonexceptional types

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Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾

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Virtual crystals and Kleber's algorithm

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A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group

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Young tableaux, Gelfand patterns, and branching rules for classical groups

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\(BC_n\)-symmetric abelian functions

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Enumeration of plane trees by branches and endpoints

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A bijection between type \(D_n^{(1)}\) crystals and rigged configurations

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Crystal structure on rigged configurations and the filling map

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Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties

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The on-line encyclopedia of integer sequences

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KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN

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Catalan Numbers

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Lattice path constructions for orthosymplectic determinantal formulas

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On bijections between 231-avoiding permutations and Dyck paths

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More bijective Catalan combinatorics on permutations and on signed permutations

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Orthogonal tableaux and an insertion algorithm for \(SO(2n+1)\)

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A Robinson-Schensted-type correspondence for a dual pair on spinors

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Identifiers

zbMATH Open document ID

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10.1016/j.disc.2019.05.020

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2312792

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