arXiv subjects

Chris Bowman

Publications and source records attributed to Chris Bowman.

23 records · Page 2Linked to original sources

arXiv2021

Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct these modules via BGG resolutions.

math.RT↗

arXiv2020

Integral Schur-Weyl duality for partition algebras

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 the partition algebra $P_r(n)$ over $k$. We also prove a similar result for the half partition algebra.

math.RT↗

arXiv2019

The uniqueness of plethystic factorisation

We prove that a plethysm product of two Schur functions can be factorised uniquely and classify homogeneous and indecomposable plethysm products.

math.RT↗

arXiv2018

An analogue of row removal for diagrammatic Cherednik algebras

We prove an analogue of James-Donkin row removal theorems for arbitrary diagrammatic Cherednik algebras. This is one of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic. As a special case, our results yield a new reduction theorem for graded decomposition numbers and extension groups for cyclotomic q-Schur algebras.

math.RT↗

arXiv2017

Generation of synthetic magnetized plasma turbulence by representation as a stochastic process

Plasma turbulence simulations are often computationally expensive with delicate numerical stability. Yet, long simulations are needed to generate uncorrelated turbulence data for studies such as microwave scattering through density perturbations. For this reason, alternative methods of producing accurate synthetic turbulence profiles via statistical methods is of interest. Such a method is proposed where the two-point covariance function of the desired turbulence is used to construct a multi-variate normal distribution. Sampling from this distribution produces random fields which are both qualitatively and quantitatively similar to the input turbulence data set. The resulting `synthetic' turbulent profiles are uncorrelated in `time' so it is useful only for scenarios that do not require such physical evolution.

physics.plasm-ph↗