Related papers: Crystal isomorphisms and Mullineux involution II
Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic…
We extend an efficient homogenization procedure based on a Haydock representation of the microscopic wave operator for the calculation of the macroscopic dielectric response of a periodic composite to the case of an arbitrary number of…
We study the natural labeling of the one dimensional representations for Ariki-Koike algebras at roots of unity. For Hecke algebras of types A and B, some of these representations can be identified with the socle of the Steinberg…
We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type A and in the representation theory of Hecke…
Lascoux stated that the type A Kostka-Foulkes polynomials K_{lambda,mu}(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, the former polynomial is a t-analogue of the multiplicity of the dominant…
We investigate deformations of skew group algebras arising from the action of the symmetric group on polynomial rings over fields of arbitrary characteristic. Over the real or complex numbers, Lusztig's graded affine Hecke algebra and…
We discuss a version of the Chevalley--Eilenberg cohomology in characteristic $2$, where the alternating cochains are replaced by symmetric ones.
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
We propose a new refinement of the McKay conjecture and we prove it for symmetric groups.
We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…
We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational…
We define the i-restriction and i-induction functors on the category O of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of…
We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and…
In this paper, we investigate a connection between convolution products for quiver Hecke algebras and tensor products for quantum groups. We give a categorification of the natural projection $ \pi_{\lambda, \mu} :…
We construct a method by which we can calculate the precision with which an algorithm identifies the shape of a cluster. We present our results for several well known clustering algorithms and suggest ways to improve performance for newer…
Generalizing the dihedral picture for G(M,M,2), we construct Hecke algebras (and present a strategy for constructing Hecke categories) and asymptotic counterparts. We think of these as associated with the complex reflection group G(M,M,N).
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
We prove that rigid cohomology can be computed as the cohomology of a site analogous to the crystalline site. Berthelot designed rigid cohomology as a common generalization of crystalline and Monsky-Washnitzer cohomology. Unfortunately,…