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The orbits of Weyl groups W(A(n)) of simple A(n) type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of A(n). Matrices transforming points of the orbits of W(An) into points of subalgebra orbits are listed for all cases n<=8 and for the infinite series of algebra-subalgebra pairs A(n) - A(n-k-1) x A(k) x U(1), A(2n) - B(n), A(2n-1) - C(n), A(2n-1) - D(n). Numerous special cases and examples are shown.
We establish a Gelfand-Naimark-Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $mathbb Z_2^n$-graded Lie supergroups.
We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null elements.
We examine the Schrodinger algebra in the framework of Berezin quantization. First, the Heisenberg-Weyl and sl(2) algebras are studied. Then the Berezin representation of the Schrodinger algebra is computed. In fact, the sl(2) piece of the Schrodinge
We investigate the structure of the Schrodinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which certain c
In this paper, first we introduce the notion of a Reynolds operator on an $n$-Lie algebra and illustrate the relationship between Reynolds operators and derivations on an $n$-Lie algebra. We give the cohomology theory of Reynolds operators on an $n$-