Abstract. The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem in a Gelfand triple with the pivot space H. This allows to employ methods of the theory of monotone operators in order to study fully discrete approximations combining a Galerkin method (including conforming finite element methods) with the backward Euler scheme. Convergence is shown eve...

In recent work ([KW1],[KW2]), 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 [KW1], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe ...

form the base of a topology on the Stone spectrum Q(R) such that Q(R) becomes a zero-dimensional, completely regular Hausdorff space. The sets QP (R) are closed-open. If the von Neumann algebra R is abelian, then the Stone spectrum Q(R) is homeomorphic to the Gelfand spectrum Ω(R) of R. For an arbitrary non-abelian unital von Neumann algebra R, the Stone spectrum can hence be regarded as a non-...

Let K be a compact Lie group acting by automorphisms on a nilpotent Lie group N . One calls (K,N) a Gelfand pair when the integrable K-invariant functions on N form a commutative algebra under convolution. We prove that in this case the coadjoint orbits for G := K nN which meet the annihilator k⊥ of the Lie algebra k of K do so in single K-orbits. This generalizes a result of the authors and R....

We prove that the following two categories of sl(n,C)-modules are equivalent: 1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; 2) the category of all subquotients of modules F ⊗ M , where F is a finite-dimensional module and M is a fixed simple generic Gelfand-Zetlin module with integral central c...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...

This is a summary of the lectures delivered on Special Functions and Linear Representation of Lie Groups at the NSF-CBMS Research Conference at East Carolina University in March 5-9, 1979. The entire lectures will be published by the American Mathematical Society as a conference monograph in Mathematics.

In 2003 Daniel K. Biss published, in the Annals of Mathematics [1], what he thought was a solution of a long standing problem culminating a discovery by Gelfand and MacPherson [3]. Six years later he was encouraged to publish an “erratum” of his prove [2], observed by Nikolai Mnëv; up to now, the homotopy type of the MacPhersonian had remained a mistery... The aim of this lecture is to convince...