Bogdan Ion

Nonsymmetric Macdonald polynomials and Demazure characters

We establish a connection between a specialization of the nonsymmetric Macdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the irreducible characters of the associated finite Lie algebra.

The Factorization Problem and the Smash Biproduct of Algebras and Coalgebras

We consider the factorization problem for bialgebras. Let L and H be algebras and coalgebras (but not necessarily bialgebras) and consider two maps R : H ⊗ L → L ⊗ H and W : L ⊗ H → H ⊗ L. We introduce a product K = LW ⋈RH and we give necessary and sufficient conditions for K to be a bialgebra. Our construction generalizes products introduced by Majid and Radford. Also, some of the pointed Hopf algebras that were recently constructed by Beattie, Dăscălescu and Grünenfelder appear as special cases.

A weight multiplicity formula for Demazure modules

We establish a formula for the weight multiplicities of Demazure modules (in particular for highest weight representations) of a complex connected algebraic group in terms of the geometry of its Langlands dual.

Weyl Modules for the Hyperspecial Current Algebra

We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type

The Structure of Frobenius Algebras and Separable Algebras

A_{2n}^{(2)}

Bicrossed Products for Finite Groups

. We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a freeness result for global Weyl modules. Furthermore, we show that the graded local Weyl modules are level one Demazure modules for the corresponding affine Lie algebra. In the last section we derive the same results for the special maximal parabolic subalgebras of the twisted affine Lie algebras not of type

The Cherednik kernel and generalized exponents

A_{2n}^{(2)}

Relative PBW Type Theorems for Symmetrically Braided Hopf Algebras

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Ketamine Inhibition of the Pentameric Ligand-Gated Ion Channel GLIC.

We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation

Group Gradings on Full Matrix Rings

R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}