On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

Definitiestudie afwegingskader : naar een klimaatbestendig Nederland : definitiestudie Fase 1, kaders voor afweging

Onzekerheid over (omvang en tempo van) de gevolgen van klimaatverandering vormt een essentieel punt bij beslissingen over de ruimtelijke inrichting. De mate waarin en de snelheid waarmee veranderingen optreden zijn niet precies bekend. Een afwegingskader geeft de overheid en de planontwikkelaar instrumenten in handen om de risico’s, de kansen, de kosten en de baten van klimaatadaptatie op verschillende onderscheiden thema’s inzichtelijk te maken. Afwegen: hoe doe je dat. Daarvoor wordt in drie stappen een kader voor gegeven

Common Algebraic Structure for the Calogero-Sutherland Models

We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis for the rational case.Comment: 7 pages, LaTeX, no figures, some text and references added, minor misprints correcte

A Computational Approach for Designing Tiger Corridors in India

Wildlife corridors are components of landscapes, which facilitate the movement of organisms and processes between intact habitat areas, and thus provide connectivity between the habitats within the landscapes. Corridors are thus regions within a given landscape that connect fragmented habitat patches within the landscape. The major concern of designing corridors as a conservation strategy is primarily to counter, and to the extent possible, mitigate the effects of habitat fragmentation and loss on the biodiversity of the landscape, as well as support continuance of land use for essential local and global economic activities in the region of reference. In this paper, we use game theory, graph theory, membership functions and chain code algorithm to model and design a set of wildlife corridors with tiger (Panthera tigris tigris) as the focal species. We identify the parameters which would affect the tiger population in a landscape complex and using the presence of these identified parameters construct a graph using the habitat patches supporting tiger presence in the landscape complex as vertices and the possible paths between them as edges. The passage of tigers through the possible paths have been modelled as an Assurance game, with tigers as an individual player. The game is played recursively as the tiger passes through each grid considered for the model. The iteration causes the tiger to choose the most suitable path signifying the emergence of adaptability. As a formal explanation of the game, we model this interaction of tiger with the parameters as deterministic finite automata, whose transition function is obtained by the game payoff.Comment: 12 pages, 5 figures, 6 tables, NGCT conference 201

Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry

Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigonometric models) potentials, their quantum versions are not exactly solvable in contrast with Calogero-Moser models. We show that quantum Inozemtsev models can be deformed to be a widest class of partly solvable (or quasi-exactly solvable) multi-particle dynamical systems. They posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A new method for identifying and solving quasi-exactly solvable systems, the method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page