1 November 2024 The Delannoy category
Nate Harman, Andrew Snowden, Noah Snyder
Author Affiliations +
Duke Math. J. 173(16): 3219-3291 (1 November 2024). DOI: 10.1215/00127094-2024-0012

Abstract

Let G be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category Rep_(G) associated to G. The present paper is a detailed study of this category, which we name the Delannoy category. We classify the simple objects, determine branching rules to open subgroups, and give a combinatorial rule for tensor products. The Delannoy category has some remarkable features: it is semisimple in all characteristics, all simples have categorical dimension ±1, and the Adams operations on its Grothendieck group are trivial. We also give a combinatorial model for Rep_(G) based on Delannoy paths.

Citation

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Nate Harman. Andrew Snowden. Noah Snyder. "The Delannoy category." Duke Math. J. 173 (16) 3219 - 3291, 1 November 2024. https://doi.org/10.1215/00127094-2024-0012

Information

Received: 6 January 2023; Revised: 10 February 2024; Published: 1 November 2024
First available in Project Euclid: 3 January 2025

MathSciNet: MR4846194
Digital Object Identifier: 10.1215/00127094-2024-0012

Subjects:
Primary: 18M25 , 20C99

Keywords: Delannoy paths , oligomorphic groups , tensor categories

Rights: Copyright © 2024 Duke University Press

Vol.173 • No. 16 • 1 November 2024
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