Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...

We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of ‘noncommutative spaces’ is the opposite of the category of C*-algebras. The second, loosely generalising Stone duality, maintains that the category of ‘pointfree spaces’ is the opposite of the cat­ egory of frames (i.e., complete lattices in which the me...

It is well known that Gelfand’s scientific interests were not limited to mathematics. One of non-mathematical field where Israel Moiseevich Gelfand worked was neurophysiology. In late 1950s, he organized neurophysiological seminar and few years later he spearheaded two neurophysiological research groups: one at the Institute of Biophysics (after 1967, this group moved to the Institute for the P...

We study centralizers of elements in domains. We generalize a result of the author and Small [4], showing that if A is a finitely generated noetherian domain and a ∈ A is not algebraic over the extended centre of A then the centralizer of a has Gelfand-Kirillov dimension at most one less than the Gelfand-Kirillov dimension of A. In the case that A is a finitely generated noetherian domain of GK...

The cross-cultural research abound in instruments used to measure individualism and collectivism (27 scales measures various forms of individualism and/or collectivism; Oyserman et al., 2002). The present article takes a closer look at two of the most widely used measures in this literature (Singelis, Triandis, Bhawuk, and Gelfand, 1995; Triandis and Gelfand, 1998) and hilights their psychometr...

In recent work ([9],[10]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [9], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe the o...

We generalize a result of Kostant and Wallach concerning the algebraic integrability of the Gelfand-Zeitlin vector fields to the full set of strongly regular elements in gl(n, C). We use decomposition classes to stratify the strongly regular set by subvarieties XD. We construct an étale cover ĝD of XD and show that XD and ĝD are smooth and irreducible. We then use Poisson geometry to lift the G...

A discrete DJS-hypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a generalized quantum Gelfand pair, where the role of the quantum subgroup is taken over by a two-sided coideal in the dual Hopf algebra. The paper starts with...

Inspired by work of Enright andWillenbring [EW], we prove a generalized Littlewood’s restriction formula in terms of Dirac cohomology. Our approach is to use a character formula of irreducible unitary lowest weight modules instead of the Bernstein-Gelfand-Gelfand resolution, and the proof is much simpler. We also show that our branching formula is equivalent to the formula of Enright and Willen...