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Chris Bowman

Publications and source records attributed to Chris Bowman.

At least 19 recordsLinked to original sources

The orientifold Temperley--Lieb algebra

We construct gradings on the simple modules of 2-boundary Temperley--Lieb algebras and symplectic blob algebras by realising the latter algebras as quotients of Varagnolo--Vasserot's orientifold quiver Hecke algebras. We prove that the symplectic blob algebras are graded cellular and provide a conjectural algorithm for calculating their graded decomposition matrices. In doing so, we give the first explicit family of finite-dimensional graded quotients of the orientifold quiver Hecke algebras, providing a new entry point for the structure of these algebras -- in the spirit of Libedinsky--Plaza's ``blob algebra approach'' to modular representation theory.

math.RT

Bayesian Analysis of Conventional and Ultrafast Spectroscopy Data for Investigating Detachment in the MAST-Upgrade Super-X

This paper presents the application, testing and first results of a new adaptive Bayesian inference analysis which utilises conventional and ultrafast spectroscopic measurements made in the divertor chamber to investigate the divertor physics during detachment. Validation of this software is performed prior and during analyses of results, demonstrated by compelling reproductions of ideal test cases and synthetic spectroscopic measurements. Application on real diagnostic data shows strong agreement with results from previous analysis methods. We identify unprecedented success in significant advances in time and computational efficiencies. We demonstrate a $\lesssim$1000$\times$ reduction in analysis time for spectroscopic measurements from simulated and real Super-X configurations, with the analysis technique presented in this report completing in <3 minutes. Analysis of synthetic and real diagnostic measurements identifies detachment physics in agreement with previous literature.

physics.plasm-ph

Two-dimensional inference of divertor plasma characteristics: advancements to a multi-instrument Bayesian analysis system

An integrated data analysis system based on Bayesian inference has been developed for application to data from multiple diagnostics over the two-dimensional cross-section of tokamak divertors. Tests of the divertor multi-instrument Bayesian analysis system (D-MIBAS) on a synthetic data set (including realistic experimental uncertainties) generated from SOLPS-ITER predictions of the MAST-U divertor have been performed. The resulting inference was within 6\%, 5\% and 30\% median absolute percentage error of the SOLPS-predicted electron temperature, electron density and neutral atomic hydrogen density, respectively, across a two-dimensional poloidal cross-section of the MAST-U Super-X outer divertor. To accommodate molecular contributions to Balmer emission, an advanced emission model has been developed which is shown to be crucial for inference accuracy. Our D-MIBAS system utilises a mesh aligned to poloidal magnetic flux-surfaces, throughout the divertor, with plasma parameters assigned to each mesh vertex and collectively considered in the inference. This allowed comprehensive forward models to multiple diagnostics and the inclusion of expected physics. This is shown to be important for inference precision when including molecular contributions to Balmer emission. These developments pave the way for accurate two-dimensional electron temperature, electron density and neutral atomic hydrogen density inferences for MAST-U divertor experimental data for the first time.

physics.plasm-ph

Effect of detachment on Magnum-PSI ELM-like pulses: II. Spectroscopic analysis and role of molecular assisted reactions

The linear plasma machine Magnum-PSI can replicate similar conditions to those found in a tokamak at the end of the divertor leg. A dedicated capacitor bank, in parallel to the plasma source, can release a sudden burst of energy, leading to a rapid increase in plasma temperature and density, resulting in a transient heat flux increase of half of an order of magnitude, a so called ELM-like pulse. Throughout both the steady state and the pulse, the neutral pressure in the target chamber is then increased, causing the target to transition from an attached to a detached state. In the first paper related to this study\cite{Federici} direct measurements of the plasma properties are used to qualitatively determine the effect of detachment on the ELM-like pulse. This is used to show the importance of molecular assisted reactions. Molecular processes, and especially molecular activated dissociation, are found to be important in the exchange of potential energy with the plasma, while less so in radiating the energy from the ELM-like pulse. At low target chamber pressure, the plasma generated via ionisation during the part of the ELM-like pulse with the higher temperature is more than that produced by the plasma source, a unique case in linear machines. At high target chamber pressure molecular activated recombination contributes up to a third of the total recombination rate, contributing to the reduction of the target particle flux. Some metrics that estimate the energy lost by the plasma per interactions with neutrals, potentially relevant for the portion of the tokamak divertor leg below $\sim10eV$, are then tentatively obtained.

physics.plasm-ph

The partition algebra and the plethysm coefficients II: ramified plethysm

The plethysm coefficient $p(\nu, \mu, \lambda)$ is the multiplicity of the Schur function $s_\lambda$ in the plethysm product $s_\nu \circ s_\mu$. In this paper we use Schur--Weyl duality between wreath products of symmetric groups and the ramified partition algebra to interpret an arbitrary plethysm coefficient as the multiplicity of an appropriate composition factor in the restriction of a module for the ramified partition algebra to the partition algebra. This result implies new stability phenomenon for plethysm coefficients when the first parts of $\nu$, $\mu$ and $\lambda$ are all large. In particular, it gives the first positive formula in the case when $\nu$ and $\lambda$ are arbitrary and $\mu$ has one part. Corollaries include new explicit positive formulae and combinatorial interpretations for the plethysm coefficients $p((n-b,b), (m), (mn-r,r))$, and $p((n-b,1^b), (m), (mn-r,r))$ when $m$ and $n$ are large.

math.RT

Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these algebras (including as examples the symmetric groups and generalised blob algebras) are tautologically equal to the associated $p$-Kazhdan-Lusztig polynomials, provided that the characteristic is greater than the Coxeter number. We hence give an elementary and more explicit proof of the main theorem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic Hecke algebras, thus solving Libedinsky-Plaza's categorical blob conjecture.

math.RT

The modular Weyl-Kac character formula

We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated in one degree. Each of these homogeneous representations is one-dimensional and can be cohomologically constructed via a BGG resolution involving every (infinite dimensional) standard representation of the category. We hence determine the complete first row of the inverse parabolic $p$-Kazhdan--Lusztig matrix for an arbitrary Coxeter group and an arbitrary parabolic subgroup. This generalises the Weyl--Kac character formula to all Coxeter systems (and their parabolics) and proves that this generalised formula is rigid with respect to base change to an arbitrary field.

math.RT

Splitting Kronecker squares, 2-decomposition numbers, Catalan Combinatorics, and the Saxl conjecture

While there has been some progress on the decomposition of Kronecker products of characters of the symmetric groups in recent times, results on the symmetric and alternating part of Kronecker squares are still scarce. Here, new results (and conjectures) are presented on this splitting of the squares that contribute to a refined understanding of the Kronecker squares. Furthermore, connections to 2-modular decomposition numbers, Catalan combinatorics, and to the Saxl conjecture are discussed which further motivate the study of these splittings.

math.CO

The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture

We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a simple and uniform fashion for the first time. We prove the strengthened Foulkes' conjecture for stable plethysm coefficients in an elementary fashion.

math.RT

The anti-spherical Hecke categories for Hermitian symmetric pairs

We calculate the $p$-Kazhdan--Lusztig polynomials for Hermitian symmetric pairs and prove that the corresponding anti-spherical Hecke categories categories are standard Koszul. We prove that the combinatorial invariance conjecture can be lifted to the level of graded Morita equivalences between subquotients of these Hecke categories.

math.RT

The role of plasma-molecule interactions on power and particle balance during detachment on the TCV tokamak

This paper shows experimental results from the TCV tokamak that indicate plasma-molecule interactions involving $D_2^+$ and possibly $D^-$ play an important role as sinks of energy (through hydrogenic radiation as well as dissociation) and particles during divertor detachment if low target temperatures ($< 3$ eV) are achieved. Both molecular activated recombination (MAR) and ion source reduction due to a power limitation effect are shown to be important in reducing the ion target flux during a density ramp. In contrast, the electron-ion recombination (EIR) ion sink is too small to play an important role in reducing the ion target flux. MAR or EIR do not occur during $N_2$ seeding induced detachment as the target temperatures are not sufficiently low. The impact of $D_2^+$ is shown to be underestimated in present (vibrationally unresolved) SOLPS-ITER simulations, which could result from an underestimated $D_2 + D^+ \rightarrow D_2^+ + D$ rate. The converged SOLPS-ITER simulations are post-processed with alternative reaction rates, resulting in considerable contributions of $D_2^+$ to particle and power losses as well as dissociation below the $D_2$ dissociation area. Those findings are in quantitative agreement with the experimental results.

physics.plasm-ph

An integral second fundamental theorem of invariant theory for partition algebras

We prove that the kernel of the action the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary commutative ring and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras.

math.RT