Signed Partition Algebras

Parvathi, M.

doi:10.1081/agb-120029909

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…Any such commutator is, by construction, an extension of the partition algebra action; and several have been explicitly cast as such, and used to study invariant theory. See for example [4,22]. 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 From the original physical perspective (i.e.…”

Section: Discussionmentioning

confidence: 99%

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Representation Theory of a Small Ramified Partition Algebra

Martin

2010

New Trends in Quantum Integrable Systems

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Here n ∈ N, k is a field, Sn is the symmetric group, δ ∈ k, and Pn(δ) is the partition algebra over k. Our aim in this note is to study the representation theory of a subalgebra P ⋉ n of kSn ⊗ k Pn(δ) with certain interesting combinatorial and representation theoretic properties. In Section 1 we discuss the motivating combinatorial background. In Section 2 we define P ⋉ n (see Proposition 1). In Section 3 we determine its complex representation theory.

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Section: Discussionmentioning

confidence: 99%

“…(From an invariant theory perspective this dual pair sequence has been extended below (S N , P n (N )) in a number of ways. See for example [4,22].) The complex reductive representation theory (i.e.…”

Section: Introductionmentioning

confidence: 99%

Representation Theory of a Small Ramified Partition Algebra

Martin

2010

New Trends in Quantum Integrable Systems

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“…then studied by several authors especially in recent years, see for example [Bl,Mar2,MarEl,MarWo,Pa,Xi]. Purely as a semigroup it seems that C n appeared in [Maz2].…”

Section: Introductionmentioning

confidence: 99%

“…From this interpretation it is fairly obvious that the composition of elements from C n defined above is associative. On the level of associative algebra, the partition algebra was defined in [Mar1] and then studied by several authors especially in recent years, see for example [Bl,Mar2,MarEl,MarWo,Pa,Xi]. Purely as a semigroup it seems that C n appeared in [Maz2].…”

Section: Brauer Type Semigroupsmentioning

confidence: 99%

On presentations of Brauer-type monoids

Kudryavtseva

Mazorchuk

2006

Open Mathematics

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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

Zaslavsky

2018

Electron. J. Combin.

118

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A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics.Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types:Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs.Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups — or no group.Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.

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Signed Partition Algebras

Cited by 6 publications

References 9 publications

Representation Theory of a Small Ramified Partition Algebra

Representation Theory of a Small Ramified Partition Algebra

On presentations of Brauer-type monoids

A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

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