In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings associated with nonarchimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SLn to other com...

We introduce a new class of noncommutative rings-Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Galois orders generalizes classical orders in noncommutative rings and contains many classical objects, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, assoc...

We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.

In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...

In the title compound, C(14)H(12)ClN(3)S, the dihedral angle between the terminal benzene rings is 56.6 (2)°; the benzene rings lie to the same side of the mol-ecule. The major twist in the mol-ecule occurs around the C(ar)-N bond (ar is aromatic) [C-N-C-C = 49.9 (5)°]. The configuration about the N=C bond [1.271 (4) Å] is E. The amine H atoms lie on opposite sides of the mol-ecule with one for...