Representations of quantum algebras.
Representations of quantum algebras (Addendum).
Representations of quantum algebras. The mixed case.
Representations of quantum groups and (conditionally) invariant q-difference equations
We give a systematic discussion of the relation between q-difference equations which are conditionally -invariant and subsingular vectors of Verma modules over (the Drinfeld-Jimbo q-deformation of a semisimple Lie algebra over ℂg or ℝ). We treat in detail the cases of the conformal algebra, = su(2,2), and its complexification, = sl(4). The conditionally invariant equations are the q-deformed d’Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel’fand-Gel’fand....
Representations of at the roots of unity
In this paper we study the irreducible finite dimensional representations of the quantized enveloping algebra associated to , at the roots of unity. It is known that these representations are parametrized, up to isomorphisms, by the conjugacy classes of the group . We get a complete classification of the representations corresponding to the submaximal unipotent conjugacy class and therefore a proof of the De Concini-Kac conjecture about the dimension of the -modules at the roots of in the...
Representations of solvable Lie algebras. II. Twisted group rings
Representations of the Lie ring over the ring of integers.
Representations of the quantum algebra and discrete -ultraspherical polynomials.
Representations with cohomology in the discrete spectrum of subgroups of and Lefschetz numbers
Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula.
Resolutions of singularities of varieties of Lie algebras of dimensions 3 and 4.
Restricted Lie algebras with bounded cohomology and related classes of algebras.
Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is...
Restriction to Levi subalgebras and generalization of the category
The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.
Riesz transforms for Dunkl transform
In this paper we obtain the -boundedness of Riesz transforms for the Dunkl transform for all .
Right coideal subalgebras of
We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group provided that is not a root of 1. If has a finite multiplicative order ; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel . In particular, the total number of right coideal subalgebras that contain the coradical equals ; the order of the Weyl group defined by the root system of type .
Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures
Rigidity of generalized Verma modules
We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).
Ringel-Hall algebras of hereditary pure semisimple coalgebras
We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.