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pro vyhledávání: '"Harman, Nate"'
Autor:
Harman, Nate, Snowden, Andrew
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we generalize
Externí odkaz:
http://arxiv.org/abs/2407.19132
Autor:
Harman, Nate, Mundinger, Joshua
Motivated by recent work of Peluse and Soundararajan on divisibility properties of the entries of the character tables of symmetric groups, we investigate the question: For a finite group G, when are two columns of the character table of G congruent
Externí odkaz:
http://arxiv.org/abs/2402.02312
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction is based o
Externí odkaz:
http://arxiv.org/abs/2308.06660
Autor:
Harman, Nate, Snowden, Andrew
Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these categories gener
Externí odkaz:
http://arxiv.org/abs/2304.05375
Let $G$ (resp. $H$) be the group of orientation preserving self-homeomorphisms of the unit circle (resp. real line). In previous work, the first two authors constructed pre-Tannakian categories $\underline{\mathrm{Rep}}(G)$ and $\underline{\mathrm{Re
Externí odkaz:
http://arxiv.org/abs/2303.10814
Autor:
Harman, Nate, Snowden, Andrew
Galois categories can be viewed as the combinatorial analog of Tannakian categories. We introduce the notion of pre-Galois category, which can be viewed as the combinatorial analog of pre-Tannakian categories. Given an oligomorphic group $G$, the cat
Externí odkaz:
http://arxiv.org/abs/2301.13784
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 $\underline{\mathrm{Rep}}(G)$ associated to $G$. The present paper is a detailed study of this categ
Externí odkaz:
http://arxiv.org/abs/2211.15392
Autor:
Harman, Nate, Snowden, Andrew
A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fra\"iss\'e theory, we show that there is a universal ultrahomogeneous cubic space $V$ of countable infinite dimension, which is unique up to isomorphism. The
Externí odkaz:
http://arxiv.org/abs/2207.09626
Autor:
Harman, Nate, Ryba, Christopher
Let $n$ be a positive integer, and let $\rho_n = (n, n-1, n-2, \ldots, 1)$ be the ``staircase'' partition of size $N = {n+1 \choose 2}$. The Saxl conjecture asserts that every irreducible representation $S^\lambda$ of the symmetric group $S_N$ appear
Externí odkaz:
http://arxiv.org/abs/2206.13769
Autor:
Harman, Nate, Snowden, Andrew
Given an oligomorphic group $G$ and a measure $\mu$ for $G$ (in a sense that we introduce), we define a rigid tensor category $\underline{\mathrm{Perm}}(G; \mu)$ of "permutation modules," and, in certain cases, an abelian envelope $\underline{\mathrm
Externí odkaz:
http://arxiv.org/abs/2204.04526