Fusion Rings of Loop Group Representations

Douglas, Christopher L.

doi:10.1007/s00220-013-1679-0

Cited by 10 publications

(6 citation statements)

References 15 publications

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“…For r = 2 this only leaves the case G 2 not taken care of. The paper [BK09] conjecturally described this fusion ideal as the radical of an ideal generated by three specific elements and later [Dou13] found an actual generating set consisting of the three elements…”

Section: The Lie Algebra Setupmentioning

confidence: 99%

Rank 2 fusion rings are complete intersections

Andersen¹

2017

Journal of Algebra

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Section: The Lie Algebra Setupmentioning

confidence: 99%

Rank 2 fusion rings are complete intersections

Andersen¹

2017

Journal of Algebra

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“…For an in-depth discussion of explicit generating sets for the fusion ideals, we refer the reader to the papers [6] and [12].…”

Section: Fusion Ringsmentioning

confidence: 99%

K-theory of AF-algebras from braided C*-tensor categories

Aaserud

Evans

2020

Rev. Math. Phys.

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We associate to each Temperley-Lieb-Jones C*-tensor category TLJ pδq with parameter δ in the discrete range t2 cospπ{pk`2qq : k " 1, 2, . . .u Y t2u a certain C*-algebra B of compact operators. We use the unitary braiding on TLJ pδq to equip the category Mod B of (right) Hilbert B-modules with the structure of a braided C*-tensor category. We show that TLJ pδq is equivalent, as a braided C*-tensor category, to the full subcategory Mod f B of Mod B whose objects are those modules which admit a finite orthonormal basis. Finally, we indicate how these considerations generalize to arbitrary finitely generated rigid braided C*-tensor categories.

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“…On the other hand, we have A(θ sα 0 (f ) ) = −A(θ f ). Therefore (9) A(θ sα 0 ,mn(f ) ) = −A(θ f ) for every element f in the weight lattice.…”

Section: G Acting On Itself By Conjugationmentioning

confidence: 99%

Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy

Ádem

Cantarero

Gómez

2018

Journal of Mathematical Physics

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We consider twisted equivariant K-theory for actions of a compact Lie group G on a space X where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequenceà la Segal has a simple E 2 -term expressible as invariants under the Weyl group of G. Namely, if T is a maximal torus of G, they are invariants of the π 1 (X T )-equivariant Bredon cohomology of the universal cover of X T with suitable coefficients. In the case of the inertia stack ΛY this term can be expressed using the cohomology of Y T and algebraic invariants associated to the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when Y = { * }.

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Fusion Rings of Loop Group Representations

Abstract: Abstract. We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.

Cited by 10 publications

References 15 publications

Rank 2 fusion rings are complete intersections

Rank 2 fusion rings are complete intersections

K-theory of AF-algebras from braided C*-tensor categories

Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy

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