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pro vyhledávání: '"Doty Stephen"'
Autor:
Doty, Stephen, Giaquinto, Anthony
We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.
Comment: 34 pages
Comment: 34 pages
Externí odkaz:
http://arxiv.org/abs/2307.11929
Autor:
Doty, Stephen, Giaquinto, Anthony
Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$, where $V=V(1)$ is the simple module of highest weight $1$ for the quantized enveloping algebra $\mathbf{U}(\mathfrak{sl}_2)$. We give a nu
Externí odkaz:
http://arxiv.org/abs/2306.17352
Autor:
Doty, Stephen, Giaquinto, Anthony
We give a combinatorial description of a new diagram algebra, the partial Temperley--Lieb algebra, arising as the generic centralizer algebra $\mathrm{End}_{\mathbf{U}_q(\mathfrak{gl}_2)}(V^{\otimes k})$, where $V = V(0) \oplus V(1)$ is the direct su
Externí odkaz:
http://arxiv.org/abs/2208.04296
Publikováno v:
In Journal of Algebra 1 December 2024 659:23-43
Autor:
Doty, Stephen, Giaquinto, Anthony
Publikováno v:
In Journal of Algebra 1 October 2024 655:294-332
Autor:
Doty, Stephen R.
We prove that the permutations of $\{1,\dots, n\}$ having an increasing (resp., decreasing) subsequence of length $n-r$ index a subset of the set of all $r$th Kronecker powers of $n \times n$ permutation matrices which is a basis for the linear span
Externí odkaz:
http://arxiv.org/abs/2109.00107
Autor:
Doty, Stephen, Giaquinto, Anthony
The twin group $TW_n$ on $n$ strands is the group generated by $t_1, \dots, t_{n-1}$ with defining relations $t_i^2=1$, $t_it_j = t_jt_i$ if $|i-j|>1$. We find a new instance of semisimple Schur--Weyl duality for tensor powers of a natural $n$-dimens
Externí odkaz:
http://arxiv.org/abs/2105.12875
Autor:
Doty, Stephen, Giaquinto, Anthony
Artin's braid group $B_n$ is generated by $\sigma_1, \dots, \sigma_{n-1}$ subject to the relations \[ \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1}, \quad \sigma_i\sigma_j = \sigma_j \sigma_i \text{ if } |i-j|>1. \] For complex
Externí odkaz:
http://arxiv.org/abs/2012.10439
Akademický článek
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Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of $\mathrm{GL}(V)$ and th
Externí odkaz:
http://arxiv.org/abs/1906.00457