On subgroup adapted bases for representations of the symmetric group

Koch, Robert de Mello; Ives, Norman; Stephanou, Michael

doi:10.1088/1751-8113/45/13/135204

Cited by 4 publications

(3 citation statements)

References 30 publications

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“…This limit was introduced and studied in [22,31] where it was called the displaced corners limit. The action of the symmetric group on right most boxes simplifies in this limit: after neglecting order 1/N corrections, permutations simply swap boxes they act on [22,32]. These are precisely the boxes that are to be removed and reassembled into irreducible representations of the subgroup which is why this simplification has far reaching consequences.…”

Section: Gauss Graph Basismentioning

confidence: 99%

“…Each YY symbol corresponds to a state in the carrier space of irreducible representation R. Translating each YY symbol into a vector in V ⊗n 2 +n 3 +m 1 +m 2 p , the action of the symmetric group on R becomes a simple action of permuting vectors in V ⊗n 2 +n 3 +m 1 +m 2 p . For a detailed account of this mathematical framework the reader should consult [32].…”

Section: Jhep10(2020)100 4 Dilatation Operator On Gauss Graphsmentioning

confidence: 99%

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Emergent Yang-Mills theory

Koch

Huang

Kim

et al. 2020

J. High Energ. Phys.

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We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su(2|3) sector of $$ \mathcal{N} $$ N = 4 super Yang-Mills theory, have a bare dimension ∼ N and are a linear combination of restricted Schur polynomials with p ∼ O(1) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of p giant graviton branes, which is a U(p) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder.

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Section: Gauss Graph Basismentioning

confidence: 99%

Section: Jhep10(2020)100 4 Dilatation Operator On Gauss Graphsmentioning

confidence: 99%

Emergent Yang-Mills theory

Koch

Huang

Kim

et al. 2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In general, explicit computation of the branching coefficients is a hard problem. See [39][40][41] for the recent results on the branching coefficients, and on the construction of the restricted Schur basis [42]. Likewise, it is difficult to compute G 123 , G 123 explicitly.…”

Section: Jhep05(2020)118mentioning

confidence: 99%

Three-point functions in $$ \mathcal{N} $$ = 4 SYM at finite Nc and background independence

Suzuki

2020

J. High Energ. Phys.

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We compute non-extremal three-point functions of scalar operators in N = 4 super Yang-Mills at tree-level in g YM and at finite N c , using the operator basis of the restricted Schur characters. We make use of the diagrammatic methods called quiver calculus to simplify the three-point functions. The results involve an invariant product of the generalized Racah-Wigner tensors (6j symbols). Assuming that the invariant product is written by the Littlewood-Richardson coefficients, we show that the non-extremal threepoint functions satisfy the large N c background independence; correspondence between the string excitations on AdS 5 × S 5 and those in the LLM geometry.

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From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications

Mozrzymas,

Horodecki,

Studziński

2024

Lett Math Phys

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In this paper, we present the connection of two concepts as induced representation and partially reduced irreducible representations (PRIR) appear in the context of port-based teleportation protocols. Namely, for a given finite group G with arbitrary subgroup H, we consider a particular case of matrix irreducible representations, whose restriction to the subgroup H, as a matrix representation of H, is completely reduced to diagonal block form with an irreducible representation of H in the blocks. The basic properties of such representations are given. Then as an application of this concept, we show that the spectrum of the port-based teleportation operator acting on n systems is connected in a very simple way with the spectrum of the corresponding Jucys–Murphy operator for the symmetric group $$S(n-1)\subset S(n)$$ S ( n - 1 ) ⊂ S ( n ) . This shows on the technical level relation between teleporation and one of the basic objects from the point of view of the representation theory of the symmetric group. This shows a deep connection between the central object describing properties of deterministic PBT schemes and objects appearing naturally in the abstract representation theory of the symmetric group. In particular, we present a new expression for the eigenvalues of the Jucys–Murphy operators based on the irreducible characters of the symmetric group. As an additional but not trivial result, we give also purely matrix proof of the Frobenius reciprocity theorem for characters with explicit construction of the unitary matrix that realizes the reduction in the natural basis of induced representation to the reduced one.

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On subgroup adapted bases for representations of the symmetric group

Cited by 4 publications

References 30 publications

Emergent Yang-Mills theory

Emergent Yang-Mills theory

Three-point functions in $$ \mathcal{N} $$ = 4 SYM at finite Nc and background independence

From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications

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