Verlinde Formulas for Nonsimply Connected Groups

Meinrenken, Eckhard

doi:10.1007/978-3-030-02191-7_14

Cited by 5 publications

(8 citation statements)

References 19 publications

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“…The t Ñ 0 limit of our formulae give quantization of the moduli space of semi-stable holomorphic G-bundles. In special cases, these formulas have been obtained in the literature using more geometric methods [12][13][14]. In each case, the t Ñ 0 limit of our results matches with the formulae found there.…”

Section: Quantization Of Moduli Space Of Higgs Bundlessupporting

confidence: 85%

“…t qq 1´g (A 14). Here r Z Ă Z 2 ˆZ2 is the smallest subgroup such that H 1 pΣ, r Zq contains h. Furthermore,Z T {pZ 2 ˆZ2 q p0q "This result follows easily by gauging the two Z 2 factors one after another, and using the result (A.3).…”

mentioning

confidence: 83%

“…16 The equivariant trace Tr t ph|H 0 pM d , L k qq can be computed by further introducing a Z p0q background. This restricts the sum in (3.31) to r Z invariant 14 The insertion of the symmetry generating line along S 1 changes the classical phase space to M d . Its quantization H 0 pM d , L k q gives the defect Hilbert space.…”

Section: Quantization Of Mpgqmentioning

confidence: 99%

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Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups

Gukov¹,

Du²,

Reid³

et al. 2021

Preprint

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We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose "fusion rules" can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SOp3q gauge group.

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Section: Quantization Of Moduli Space Of Higgs Bundlessupporting

confidence: 85%

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confidence: 83%

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Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups

Gukov¹,

Du²,

Reid³

et al. 2021

Preprint

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“…We know from the proof of corollary 3.5 that the restricted map First, by choosing both g and L to be the unit element of G C R , we see that M * is a proper subset of M. Next, let us recall that the center Z(G) is the intersection of all maximal tori of G, and for a fixed maximal torus G 0 one can find (see e.g. [42]) another one,…”

Section: Fehérmentioning

confidence: 99%

Poisson–Lie analogues of spin Sutherland models revisited

Fehér

2024

J. Phys. A: Math. Theor.

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Some generalizations of spin Sutherland models descend from `master integrable systems' living on Heisenberg doubles of compact semisimple Lie groups. The master systems represent Poisson--Lie counterparts of the systems of free motion modeled on the respective cotangent bundles and their reduction relies on taking quotient with respect to a suitable conjugation action of the compact Lie group. We present an enhanced exposition of the reductions and prove rigorously for the first time that the reduced systems possess the property of degenerate integrability on the dense open subset of the Poisson quotient space corresponding to the principal orbit type for the pertinent group action. After restriction to a smaller dense open subset, degenerate integrability on the generic symplectic leaves is demonstrated as well. The paper also contains a novel description of the reduced Poisson structure and a careful elaboration of the scaling limit whereby our reduced systems turn into the spin Sutherland models.

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“…By Lemma 4.1, the order of the obstruction class ∂DD(G) equals the order of ℓ f • φ * z, where z generates H 3 (G; Z). The order of φ * z was computed directly in [11] (see also [15,Proposition 4.1]) for each compact simple Lie group, and is found to coincide with the basic level ℓ b (see Section 2 p. 3). Hence, the obstruction φ * x has order ℓ b /ℓ f .…”

Section: And Thusmentioning

confidence: 99%