A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
We construct essentially all the irreducible modules for the multiparameter quantum function algebraF?φ[G], whereG is a simple simply connected complex algebraic group, and ? is a root of unity.
We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-type root system.
Let ζ-1/2 be the inverse on the set of regular elements ofu of a square root of the discriminant of.
We construct a one-parameter family of flat connections ?κ on h with values in any finite-dimensional g-module V and simple poles on the root hyperplanes.
Simple modules over the multiparameter quantum function algebra at roots of 1
Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots.
The residues of ?κ are the Casimirs κα of the subalgebra sslα2 ? g corresponding to the roots of g.
A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven.
Except for tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of the real roots of several univariate polynomials.
A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical
Let B be a Borel subgroup of G; we write U for the unipotent radical of B and u for the Lie algebra of U.
We also construct the ideal of definition of such an orbital variety up to taking the radical.
Antioxidant activity of melatonin and some new melatonin analogue indole derivatives were investigated, using lipid peroxidation and superoxide anion radical scavenger activity assays, in rat liver tissue homogenate.
Further, they exhibited moderate concentration-dependent inhibition of the DPPH radical.