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Panyushev D.I.,Independent University of Moscow
Selecta Mathematica, New Series | Year: 2010

Let G be a simple algebraic group and B a Borel subgroup. We consider generalisations of Lusztig's q-analogues of weight multiplicity, where the set of positive roots is replaced with the multiset of weights of a B-submodule N of an arbitrary finite-dimensional G-module V. The corresponding polynomials in q are called generalised Kostka-Foulkes polynomials (gKF). We prove vanishing theorems for the cohomology of line bundles on G × BN and derive from this a sufficient condition for the non-negativity of the coefficients of gKF. We also consider in detail the case in which V is the simple G-module whose highest weight is the short dominant root and N is the B-submodule whose weights are all short positive roots. © 2010 Birkhäuser / Springer Basel AG. Source

Mejia-Monasterio C.,University of Helsinki | Mejia-Monasterio C.,Technical University of Madrid | Oshanin G.,University Pierre and Marie Curie | Oshanin G.,Independent University of Moscow
Soft Matter | Year: 2011

A particle driven by an external force in a molecular crowding environment - a quiescent bath of other particles, makes their spatial distribution inhomogeneous: the bath particles accumulate in front of the biased particle (BP) and are depleted behind. In fact, a BP travels together with the inhomogeneity it creates. A natural question is what will happen with two BPs when they appear sufficiently close to each other such that the inhomogeneities around each of them start to interfere? In quest for the answer we examine here, via Monte Carlo simulations, the dynamics of two BPs in a lattice gas of bath particles. We observe that for a sufficiently dense medium, surprisingly, both BPs spend most of the time together which signifies that the interference of the microstructural inhomogeneities results in effectively attractive interactions between them. Such statistical pairing of BPs minimizes the size of the inhomogeneity and hence reduces the frictional drag force exerted on the BPs by the medium. As a result, in some configurations the center-of-mass of a pair of BPs propagates faster than a single isolated BP. These jamming-induced forces are very different from fundamental physical interactions, exist only in presence of an external force, and require the presence of a quiescent bath to mediate the interactions between the driven particles. © 2011 The Royal Society of Chemistry. Source

Olshanski G.,Independent University of Moscow
Electronic Journal of Combinatorics | Year: 2010

Let Mn stand for the Plancherel measure on Yn, the set of Young diagrams with n boxes. A recent result of R. P. Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with respect to Mn depends on n polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel measure. Source

Sossinsky A.B.,Independent University of Moscow
Russian Journal of Mathematical Physics | Year: 2016

We describe a discrete 3D model of ideal gas based on the idea that, on the microscopic level, the particles move randomly (as in ASEP models), instead of obeying Newton’s laws as prescribed by Boltzmann. © 2016, Pleiades Publishing, Ltd. Source

Sossinsky A.B.,Independent University of Moscow
Russian Journal of Mathematical Physics | Year: 2012

This article is a continuation of the study of new types of knot energy undertaken in [1, 2] (but is formally independent of those articles); it describes some experiments with mechanical models of knots (that we call twisted wire knots), contains rigorous definitions of their mathematical counterparts, formulations of a series of problems and conjectures. Different energy functionals for various classes of knot types and the corresponding normal forms are discussed and compared. © 2012 Pleiades Publishing, Ltd. Source

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