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Register a new userBranching rules for the Weyl group orbits of the Lie algebra A(n)
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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.
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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.
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