Related papers: On the unitarization of linear representations of …

We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.

We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…

A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…

We discuss invertibility properties for entire finite-energy solutions of the regularized version of a singular Liouvillle equation.

We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.

We show that weighted path orders are special instances of a variant of semantic path orders. Exploiting this fact, we introduce a generalization of weighted path orders that goes beyond the realm of simple termination. Experimental data…

We prove some weighted $L_p$ estimates for generalized harmonic extensions in the half-space.

We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.

In this paper we study the Gan-Gross-Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.

For any finite-dimensional simple Lie algebra $\mathfrak{g}$ and commutative associative algebra $S$ of finite type, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S$ with bounded weight…

We study the existence of unitriangular basic sets for the symmetric group which behave nicely with respect to the Mullineux involution. Such sets give a natural labelling for the modular irreducible representations. We show that, for any…

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices.

Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…

We consider the set of Baire 1 functions endowed with the pointwise partial ordering and investigate the structure of the linearly ordered subsets.

In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study…