Two actions of the Hecke algebra of type A on the corresponding polynomial ring are introduced. Both are deformations of the natural action of the symmetric group on polynomials, and keep symmetric functions invariant. An explicit combinatorial formula is given for the resulting graded characters on the coinvariant algebra.

Abstract An explicit description of the ring rational polynomials in r indeterminates as a representation Lie algebra endomorphisms k -th exterior power countably infinite-dimensional vector space is given. Our based on results by Laksov and Throup concerning symmetric structure polynomial ring. are approximate versions vertex operators occurring celebrated bosonic representation, due to Date, ...

F [D] of Weyl type was defined and studied, where A is a commutative associative algebra with an identity element over a field F of arbitrary characteristic, and F [D] is the polynomial algebra of a commutative derivation subalgebra D of A. The 2-cocycles of a class of A[D] were determined by Su. In the present paper, we determine the 2-cocycles of a class of Lie superalgebras of Weyl type over...

The Cayley Hamilton theorem on the characteristic polynomial of a matrix A and Frobenius’ theorem on minimal polynomial of A are deduced from the familiar Laplace transform formula L(eAt) = (sI − A)−1. This formula is extended to a formal power series ring over an algebraically closed field of characteristic 0, so that the argument applies in the more general setting of matrices over a field of...