On Brauer algebra simple modules over the complex field

Visscher, Maud De; Martin, Paul

doi:10.1090/tran/6716

Cited by 4 publications

(2 citation statements)

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“…The following result says that the seminormal representations of the quotient algebras Q K r are obtained as truncations of the seminormal representations of the diagram algebras A F r . The application of this result to the Brauer algebras and their quotients acting on orthogonal or symplectic tensor space recovers a well-known phenomenon, which is implicit in [41,34,44], and explicit in [9,Theorem 5.4.3]. See also [14].…”

Section: Supplements On Quotient Towersmentioning

confidence: 54%

The Cellular Second Fundamental Theorem of Invariant Theory for Classical Groups

Bowman

Enyang

Goodman

2018

International Mathematics Research Notices

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We prove that the kernel of the action of the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary integral domain and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras.

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Section: Supplements On Quotient Towersmentioning

confidence: 54%

The Cellular Second Fundamental Theorem of Invariant Theory for Classical Groups

Bowman

Enyang

Goodman

2018

International Mathematics Research Notices

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“…However the case of characteristic p > 0 remains essentially open (cf. [20,9]), and it is this problem that motivates the present work.…”

Section: Introductionmentioning

confidence: 99%

On central idempotents in the Brauer algebra

2018

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We provide a method for constructing central idempotents in the Brauer algebra relating to the splitting of certain short exact sequences. We also determine some of the primitive central idempotents, and relate properties of the idempotents to known facts about the representation theory of the algebra.We will refer to these three cases as northern horizontal arcs, southern horizontal arcs and propagating lines respectively. This allows us to define the following subsets of J n : J n [ ] = A ∈ J n | A contains precisely components a i such that tp(a i ) = P , andIn other words J n [ ] can be thought of as the set of diagrams with precisely propagating lines, and J n ( ) as the set of diagrams with at most propagating lines.Multiplication in B n is defined by vertical concatenation of diagrams. Given A, B ∈ J n we compute AB by drawing A on top of B so that the southern nodes of A and the northern nodes Then a basis of B n over K is given byWe analogously define J n [ ] = {A | A ∈ J n [ ]}, J n ( ) = {A | A ∈ J n ( )}, and J n ( ) = B n J n ( )B n .Note that since all elements of J n [n] are generated by the σ i , we have J n [n] = J n [n].

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