Related papers: Representation formula for discrete indefinite aff…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
A smooth affine minimal surface with indefinite metric can be obtained from a pair of smooth non-intersecting spatial curves by Lelieuvre's formulas. These surfaces may present singularities, which are generically cuspidal edges and…
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.
We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…
We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(T_p M) for all p in M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we…
We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine Hecke algebras.
We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class…
Our goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations…
We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of…
General semifinite factor representations of the diffeomorphism group of euclidean space are constructed by means of a canonical correspondence with the finite factor representations of the inductive limit unitary group. This construction…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf $*$-algebras. Moreover, we characterize invariant inner products…
In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group $\mathrm{SL}_2(\mathbb{F}_q[t])$ and with values in absolutely irreducible…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…
It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of…
We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.
We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…
We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle of the form $(1...n)$ we derive a straightforward process…