Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Westbury, Bruce"'
Autor:
Westbury, Bruce W., Zinn-Justin, Paul
We give a uniform trigonometric $R$-matrix for the adjoint representations on the exceptional series. The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras i
Externí odkaz:
http://arxiv.org/abs/2406.01348
Many continuous reaction-diffusion models on $\mathbb{Z}$ (annihilating or coalescing random walks, exclusion processes, voter models) admit a rich set of Markov duality functions which determine the single time distribution. A common feature of thes
Externí odkaz:
http://arxiv.org/abs/2212.12944
Autor:
Westbury, Bruce W.
We introduce quantum skein relations for a family of ribbon categories parametrised by the projective plane over $\bQ$. There are thirteen points for which the ribbon category admits a ribbon functor to a category of invariant tensors for a quantised
Externí odkaz:
http://arxiv.org/abs/2211.04270
Autor:
Savage, Alistair, Westbury, Bruce W.
We introduce a graphical calculus for the representation theory of the quantized enveloping algebra of type $F_4$. We do this by giving a diagrammatic description of the category of invariant tensors on the 26-dimensional fundamental representation.<
Externí odkaz:
http://arxiv.org/abs/2204.11976
Autor:
Savage, Alistair, Westbury, Bruce W.
Publikováno v:
In Journal of Pure and Applied Algebra November 2024 228(11)
Publikováno v:
European Journal of Combinatorics (2022)
We study the enumerative and analytic properties of some sequences constructed using tensor invariant theory. The octant sequences are constructed from the exceptional Lie group $G_2$ and the quadrant sequences from the special linear group $SL(3)$.
Externí odkaz:
http://arxiv.org/abs/2110.13753
We study two families of sequences, listed in the On-Line Encyclopedia of Integer Sequences (OEIS), which are associated to invariant theory of Lie algebras. For the first family, we prove combinatorially that the sequences A059710 and A108307 are re
Externí odkaz:
http://arxiv.org/abs/1911.10288
Autor:
Westbury, Bruce W.
We give a new proof of the cyclic sieving phenomena for promotion on rectangular standard tableaux. This uses an action of the cactus groups in the seminormal bases of the irreducible representations of the Hecke algebras.
Externí odkaz:
http://arxiv.org/abs/1906.07146
Using Henriques' and Kamnitzer's cactus groups, Sch\"utzenberger's promotion and evacuation operators on standard Young tableaux can be generalised in a very natural way to operators acting on highest weight words in tensor products of crystals. For
Externí odkaz:
http://arxiv.org/abs/1804.06736
Publikováno v:
In European Journal of Combinatorics October 2022 105