Representation Theory

Abstract

Representation theory: a first eourse / William Fulton and Joe Harris. p. em. -(Graduate texts in mathematies) IncJudes bibliographieal referenees and index. 1. Representations of groups. 2. Representations of Algebras. 3. Lie Groups. 4. Lie algebras. 1. Harris, Joe. II. Tîtle.

Duality for spherical representations in exceptional theta correspondences

“…We have V (nω) SU 2,l = V (n, n, 0). By [FH,(25.39) on p. 427]), the restriction of V n,0 to Sp 6 decomposes as V n,0 ∼ = ⊕ c≤n V (c, c, 0). Hence V (n, n, 0) ∼ = V n,0 /V n−1,0 , as SU 2,s -modules, and by Lemma 6.1,…”

Level-rank duality of D-branes on the SU(N) group manifold

“…For N + K not prime, we must use a different approach. The dimension of an arbitrary irreducible representation of su(N) can be written as the determinant of an ℓ 1 × ℓ 1 matrix [35] dim…”

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

“…The action of the exponential e Γ on ξ allows to compute χ g Λ (ξ), the so called specialization of the character at ξ. In the case of Lie algebras, the group character definition, given in the representation theory of Lie groups (see [27]), is simply related to that of the formal character (as explained in section 13.4.1 of [16]), so from now on we will refer to it as the character associated to a h.w. representation of the algebra.…”

“…The last condition makes possible to interpret Λ = m i=1 u i ǫ i as a weight of su(m), where ǫ 1 , .., ǫ m is an orthonormal basis of the Euclidean space R m [44,27,16]. In terms of Dynkin labels Λ can be rewritten as Λ =…”

“…The cyclic permutation orbifold in the next section is made with respect to this discrete symmetry group Z m of u(1) Km,p . 27) with b ∈ {0, .., 2mp} and K (q) b (w|τ ) the characters of the Γ θ -RCFT u(1) q , q odd, given by:…”