Irreducible Linear Group-Subgroup Pairs with the Same Invariants

Symmetry classes of polynomials associated with the dihedral group

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

On the Restriction of Characters of Special Linear Groups of Dimension Three

IRREDUCIBLE CONGRUENCES OVER GF(p)

with coefficients belonging to the same field. Two irreducible m-ic congruences are said to belong to the same conjugate set if one of them can be transformed into the other by a transformation of G. The number of distinct irreducible congruences in a conjugate set will be referred to as the order of the conjugate set. Since the order of the group G is p(pi — l), it follows that the order of an...

Dual Canonical Bases for the Quantum Special Linear Group and Invariant Subalgebras

Abstract. A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible Uq(sl(n))-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quan...

Arithmetic invariants of discrete Langlands parameters

Let G be a reductive algebraic group over the local field k. The local Langlands conjecture predicts that the irreducible complex representations π of the locally compact group G(k) can be parametrized by objects of an arithmetic nature: homomorphisms φ from the Weil-Deligne group of k to the complex L-group of G, together with an irreducible representation ρ of the component group of the centr...