1 Introduction The Verlinde formula is a remarkable—and potentially very useful—new tool in the geometry of algebraic curves which is borrowed from conformal field theory. In the first instance it is a trigonometric expression which assigns a natural number N l (G, g) to data consisting of a semisimple algebraic group G, a nonnegative integer g and an auxiliary integer l ∈ Z. In physics N l (G,...

We study the relationship between l-groups, Bézout domains, and MV -algebras. Our main motivation and starting point has been the Jaffard-Ohm correspondence between Abelian l-groups and Bézout domains ¶ μ 3 ́ Bézout domains with non-zero unit radical ¶ μ 3 ́ Unital l-groups ¶ μ 3 ́ MV -algebras ©© ©© ©© © HHHHHH ——————————– and Mundici’s equivalence between Abelian unital l-groups and MV -algebras...

We investigate the shellability of polyhedral join $\mathcal{Z}^*_M (K, L)$ simplicial complexes $K, M$ and a subcomplex $L \subset K$. give sufficient conditions necessary on $(K, for being shellable. In particular, we show that some pairs L)$, becomes shellable regardless whether $M$ is or not. Polyhedral joins can be applied to graph theory as independence complex certain generalized version...

We study certain ltrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warreld. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily simp...

One purpose is to isolate techniques and results in representation theory which do not depend upon additional structure of the groups. Much can be done in the representation theory of compact groups without anything more than the compactness. Similarly, the discrete decomposition of L(Γ\G) for compact quotients Γ\G depends upon nothing more than compactness. Schur orthogonality and inner produc...

| In this paper we discuss topics in harmonic analysis and representation theory related to two diierent real forms G=H and G c =H of a complex semisimple symmetric space G C =H C. We connect representations of G and G c using the theory of involutive representations of semigroups and reeection symmetry. We discuss how to generalize the Segal-Bargmann transform to real forms of bounded symmetri...

A n a q u e o u s so lu t ion of u r a n y l ace t a t e was first e m p l o y e d as a n e l ec t ron s ta in by W a t s o n (1958). W e h a v e f o u n d t h a t this s ta in , a l t h o u g h f r e q u e n t l y effective, is capr ic ious . T h e s ta in m a y no t inc rease con t r a s t of a g iven spec imen , a n d m a y , in o the r ins tances , l eave u n d e s i r a b l e c o n t a m i...

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