Transitioning between tableaux and spider bases for Specht modules

2019/11/12 by Mee Seong Im, Im, Mee Seong, Jieru Zhu +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1911.05049

openalex publication_date 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Regarding the Specht modules associated to the two-row partition (n,n), we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the A₁-web basis (i.e. cup diagrams), and prove that the entries in this matrix are positive in the upper-triangular portion with respect to a certain partial order.

Related

• M-diagram basis of the Specht module for (n,n,n)
• A combinatorial model for the transition matrix between the Specht and web bases
• The transition matrix between the Specht and web bases is unipotent with additional vanishing entries
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• A proof of the Murnaghan--Nakayama rule using Specht modules and tableau combinatorics