Representations of Twisted Yangians of Types B, C, D: Ii

Guay, Nicolas; Regelskis, Vidas; Wendlandt, Curtis

doi:10.1007/s00031-019-09514-x

Cited by 5 publications

(5 citation statements)

References 30 publications

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“…Unfortunately, the representation theory of X(so 6 , so 5 ) has hardly been studied in the literature. In [51,52] only twisted Yangians with diagonal K-matrix were studied. Therefore the twisted Yangian X(so 6 , so 5 ) was ignored (see the explicit form of the K-matrix (5.50)).…”

Section: Twisted Yangiansmentioning

confidence: 99%

Spin chain overlaps and the twisted Yangian

Leeuw

Gombor

Kristjansen³

et al. 2020

J. High Energ. Phys.

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Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the SO(6) spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of so(5). The latter play the role of boundary states in a domain wall version of N = 4 SYM theory which has nonvanishing, SO(5) symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

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Section: Twisted Yangiansmentioning

confidence: 99%

Spin chain overlaps and the twisted Yangian

Leeuw

Gombor

Kristjansen³

et al. 2020

J. High Energ. Phys.

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“…The twisted Yangian Y σ should coincide with its algebraic counterpart, which can be traced back to Cherednik's work [Ch84]; see [M07,GRWa,GRWb]. It is our hope that Theorem D will serve as a small step towards a geometric theory of (g, K R )-modules, which in turn will shed light on that of unitary representations of the associated real simple group.…”

Section: Introductionmentioning

confidence: 87%

Quiver varieties and symmetric pairs

2019

Represent. Theory

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We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram isomorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type A case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.

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“…It will be interpreted as the boundary quantum space of the open spin chain. The Lemma below rephrases Lemma 2.3 in [GRW1] and Lemma 5.4 in [GRW2]. when n ≥ 1 and G is type CI, or n ≥ 2 and G is of type DIII, and (3.27) when n = 2, and (3.28)…”

Section: Introduce a Rational Function Acting Onmentioning

confidence: 99%

“…The twisted Yangian X ρ (g 2n , g θ 2n ) tw . We now focus on the Extended twisted Yangian X ρ (g 2n , g θ 2n ) tw and its representation theory adhering closely to [GR,GRW1,GRW2]. As before, we drop the "Extended" part of the name to simplify the notation.…”

Section: Introduce a Rational Function Acting Onmentioning

confidence: 99%

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Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains

Gerrard

Regelskis

2020

Nuclear Physics B

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We present a nested algebraic Bethe ansatz for one-dimensional open so 2n -and sp 2n -symmetric spin chains with diagonal boundary conditions and described by the extended twisted Yangian. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so 2n -or sp 2n -symmetric open spin chain to that of a gl n -symmetric open spin chain. We explicitly derive the structure of Bethe vectors and the nested Bethe equations.

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Representations of Twisted Yangians of Types B, C, D: Ii

Cited by 5 publications

References 30 publications

Spin chain overlaps and the twisted Yangian

Spin chain overlaps and the twisted Yangian

Quiver varieties and symmetric pairs

Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains

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