A Soergel-like category for complex reflection groups of rank one

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group $W$ and a free module of rank $|W| (|W|-1)+1$ over the base ring. We also show that it is a generically semisimple algebra if defined over the complex numbers.Comment: 24 pages. Comments welcome

Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n, r) for 3 <= r < n

We categorify the extended affine Hecke algebra and the affine quantum Schur algebra S(n, r) for 3 <= r < n, using results on diagrammatic categorification in affine type A by Elias-Williamson, that extend the work of Elias-Khovanov for finite type A, and Khovanov-Lauda respectively. We also define 2-representations of these categorifications on an extension of the 2-category of affine (singular) Soergel bimodules. These results are the affine analogue of the results in [28].FCT-Fundacao para a Ciencia e a Tecnologia [PTDC/MAT/101503/2008]New Geometry and Topologyinfo:eu-repo/semantics/publishedVersio

A diagrammatic categorification of the affine q-Schur algebra S(n,n) for n > 2

This is a follow-up to the paper in which we categorified the affine quantum Schur algebra S(n,r) for 2 < r < n, using a quotient of Khovanov and Lauda's categorification of the affine quantum sl_n. In this paper we categorify S(n,n) for n > 2, using an extension of the aforementioned quotient.info:eu-repo/semantics/publishedVersio

A united statement of the global chiropractic research community against the pseudoscientific claim that chiropractic care boosts immunity.

BACKGROUND: In the midst of the coronavirus pandemic, the International Chiropractors Association (ICA) posted reports claiming that chiropractic care can impact the immune system. These claims clash with recommendations from the World Health Organization and World Federation of Chiropractic. We discuss the scientific validity of the claims made in these ICA reports. MAIN BODY: We reviewed the two reports posted by the ICA on their website on March 20 and March 28, 2020. We explored the method used to develop the claim that chiropractic adjustments impact the immune system and discuss the scientific merit of that claim. We provide a response to the ICA reports and explain why this claim lacks scientific credibility and is dangerous to the public. More than 150 researchers from 11 countries reviewed and endorsed our response. CONCLUSION: In their reports, the ICA provided no valid clinical scientific evidence that chiropractic care can impact the immune system. We call on regulatory authorities and professional leaders to take robust political and regulatory action against those claiming that chiropractic adjustments have a clinical impact on the immune system

Measurement of the Splitting Function in &ITpp &ITand Pb-Pb Collisions at root&ITsNN&IT=5.02 TeV

Data from heavy ion collisions suggest that the evolution of a parton shower is modified by interactions with the color charges in the dense partonic medium created in these collisions, but it is not known where in the shower evolution the modifications occur. The momentum ratio of the two leading partons, resolved as subjets, provides information about the parton shower evolution. This substructure observable, known as the splitting function, reflects the process of a parton splitting into two other partons and has been measured for jets with transverse momentum between 140 and 500 GeV, in pp and PbPb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair. In central PbPb collisions, the splitting function indicates a more unbalanced momentum ratio, compared to peripheral PbPb and pp collisions.. The measurements are compared to various predictions from event generators and analytical calculations.Peer reviewe