Related papers: Relationships between plethysm coefficients
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general…
We construct families of representations for quantum groups over $\mathbb{Z}[v,v^{-1}]$-algebras that interpolate between Weyl modules and tilting modules. These families might be candidates for objects with characters satisfying the {\em…
We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli…
We discuss modular family symmetry in effective theories based on generic properties of bottom-up local F-theory inspired GUTs broken by fluxes, which we refer to as Fluxed GUTs. We argue that the Yukawa couplings will depend on the complex…
We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…
We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly supported, provided one uses the correct local system of…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been…
In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…
We construct quantization functors of quasi-Lie bialgebras. We establish a bijection between this set of quantization functors, modulo equivalence and twist equivalence, and the set of quantization functors of Lie bialgebras, modulo…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We…
We study bounds for correlation sums of automorphic coefficients on $\mathrm{GL}_{3,\mathbb{Q}}$ with trace functions of composite moduli. This is a sequel to our previous works with E. Kowalski and W. Sawin.
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…