Eigenvalues of Casimir invariants for unitary irreps of

Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)

“…We now aim to prove the following weaker version of the Theorem above, using the Lemma: Proof: From the decomposition (73) this is enough to prove part (i) of the proposition. As to the second part we proceed as in the proof of Theorem 2 and suppose 0 = w + ∈ V ⊗ V (Λ) is also a maximal weight vector of the same weight ν.…”

“…Note that strictly speaking, this formula is only valid on the Zariski dense subset as mentioned earlier. For more on the general case, see [72,73]. In graded index notation, we furthermore have γr = (−1)…”

Algebraic properties of an integrable t-J model with impurities

“…( 32). Now by using the relations (30,31,50) and looking only for those terms which give a vector proportional to X h we find that…”

“…A general theorem states [29] that tensor products of type I unitary representations are always completely reducible into representations which are also of type I. Moreover, since the module which acts for the impurity spaces is typical it follows from [31] (see Proposition 2) that all the modules occuring in the decomposition of the tensor product space are in fact typical.…”