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.
Some exceptional compact matrix pseudogroups
Some remarks on quantum and braided group gauge theory
We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.
Spectrum of the quantized Weyl algebra. (Spectre de l'algèbre de Weyl quantique.)
Spherical functions on a complex classical quantum group
Spherical functions on a family of quantum 3-spheres
Spin chain connected to the quantum superalgebra .
Squared Hopf algebras and reconstruction theorems
Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained from a squared...
Statistics and quantum group symmetries
Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.
Strange phenomena related to ordering problems in quantizations.