Symmetry, Representations, and Invariants

By R. Goodman, Nolan Wallach. 2009

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Citations in the corpus

On the representation theory of partial Brauer algebras (2012, neutral): “ of the Ok-module V ⊗m deﬁned above. Proposition 19. The algebra Rm coincides with EndO k (V⊗m). To prove this statement we will need some facts from the classical representation theory of Ok. We use [GoWa] as a general reference. Simple Ok-modules appearing in V ⊗l, l ∈ N 0, are indexes by integer ”
WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT $L$ -FUNCTIONS (2013, neutral): “ G′(C)) of highest weight (µ,µv) (resp. (λ,λv)). (Here the check “v” denotes taking the contragredient representation.) It is isomorphic to its complex conjugate contragredient. Lemma 2.1 (See, e.g., [12], Thm. 8.1.1). With the above notation, the following assertions are equivalent: (1) µ1 ≥ −λn−1 ”
NOTES ON THE ARITHMETIC OF HILBERT MODULAR FORMS (2011, neutral): “ν2 j=0 cjsj) = cν1. Proof. This is easy to verify and we omit the proof. Let us mention that this is a special case of well-known classical branching laws from GLn(C) to GLn−1(C); see Goodman-Wallach [17]. The SO(2)-types of Eν, as well as Ev ν, are given by: Ev ν|K1 2 = Eν|K1 2 = θ−(ν 1−ν2) ⊕θ−(ν1−”