Splitting Kronecker squares, 2-decomposition numbers, Catalan combinatorics, and the Saxl conjecture

DOI10.5802/alco.294zbMath1528.05002arXiv2202.03066OpenAlexW4386254140WikidataQ122917307 ScholiaQ122917307MaRDI QIDQ6088377

Christopher Bowman, Christine Bessenrodt

Publication date: 14 December 2023

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.03066

zbMATH Keywords

symmetric groupsKronecker productdecomposition numberscharacter theoryCatalan combinatoricssymmetric tensor squares

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Symmetric groups (20B30) Combinatorial aspects of groups and algebras (05E16)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie superalgebras and some characters of \(S_n\).
• A diagrammatic approach to Kronecker squares
• Bounds on certain classes of Kronecker and \(q\)-binomial coefficients
• Kronecker coefficients for one hook shape
• Nonvanishing of Kronecker coefficients for rectangular shapes.
• Expressions for Catalan Kronecker products
• On rectangular Kronecker coefficients.
• Irreducibility of tensor squares, symmetric squares and alternating squares.
• The spectra of quantum states and the Kronecker coefficients of the symmetric group
• Nonzero Kronecker coefficients and what they tell us about spectra
• Kronecker products, characters, partitions, and the tensor square conjectures
• The complex characters of the symmetric groups that remain irreducible in subgroups
• On the Kronecker product of \(S_n\) characters
• The character covering numbers of the alternating groups
• The representation theory of the symmetric groups
• Character theory of finite groups
• On the irreducibility of alternating powers and symmetric squares
• On the Kronecker product of Schur functions of two row shapes
• Irreducibility of alternating and symmetric squares
• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
• Irreducible modules for symmetric groups that are summands of their exterior square
• Critical classes, Kronecker products of spin characters, and the Saxl conjecture
• Multiplicity-free Kronecker products of characters of the symmetric groups
• A note on skew characters of symmetric groups
• Geometric complexity theory and matrix powering
• Recoupling coefficients and quantum entropies
• A formula for the Kronecker products of Schur functions of hook shapes
• Vanishing symmetric Kronecker coefficients
• The Saxl conjecture and the dominance order
• On the Durfee size of Kronecker products of characters of the symmetric group and its double covers.
• Rectangular Kronecker coefficients and plethysms in geometric complexity theory
• A combinatorial interpretation for the coefficients in the Kronecker product \(s_{(n-p,p)} \ast s_\lambda\)
• KRONECKER COEFFICIENTS VIA SYMMETRIC FUNCTIONS AND CONSTANT TERM IDENTITIES
• Permanent versus determinant: Not via saturations
• An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP}\neq\mathbf{VNP}$
• A note on certain Kronecker coefficients
• Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type
• No occurrence obstructions in geometric complexity theory
• The uniqueness of plethystic factorisation
• Proceedings of the International Congress of Mathematicians (ICM 2018)
• A simplified Kronecker rule for one hook shape
• A Course in Finite Group Representation Theory
• On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring
• On Kronecker products of spin characters of the double covers of the symmetric groups.

This page was built for publication: Splitting Kronecker squares, 2-decomposition numbers, Catalan combinatorics, and the Saxl conjecture