Representations of the quantum algebra and discrete -ultraspherical polynomials.
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.
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...
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 .
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.
R-matrix brackets and their quantization
Root vectors in quantum groups.
Rosso's form and quantized Kac Moody algebras.
Semicanonical bases and preprojective algebras
Semi-centre de l'algèbre enveloppante d'une sous-algèbre parabolique d'une algèbre de Lie semi-simple
Semilinear relations and *-representations of deformations of so(3)
We study a family of commuting selfadjoint operators , which satisfy, together with the operators of the family , semilinear relations , (, , are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra .
Separation of variables in the quantum integrable models related to the Yangian
Skein quantization of Poisson algebras of loops on surfaces
Skein theory for -quantum invariants.
Sklyanin determinant for reflection algebra.
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Solutions to the XXX type Bethe ansatz equations and flag varieties
We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and...
Solvable lattice model and representation theory of quantum affine algebras.
Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation.