New Bases for the Decomposition of the Graded Left Regular Representation of the Reflection Groups of Type B and D

Allen, Edward E.

doi:10.1006/jabr.1995.1080

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Introduction2

This Lemma Implies That1

A Multigrading Of C[x] and Two Bases1

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1997

2011

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Cited by 4 publications

(9 citation statements)

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“…It should be noted that there are analogues to Theorem 1.1 for the complex reflection groups as well as an analogue in terms of descent monomials (see [4]). …”

Section: This Lemma Implies Thatmentioning

confidence: 96%

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Bitableaux Bases for the Diagonally Invariant Polynomial Quotient Rings

Allen

1997

Advances in Mathematics

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“…It should be noted that there are analogues to Theorem 1.1 for the complex reflection groups as well as an analogue in terms of descent monomials (see [4]). …”

Section: This Lemma Implies Thatmentioning

confidence: 96%

“…The column stabilizer N(I ) of I is the product group [1,2,3] _S [4,5,6] _S [7,8] _S [9,10] and N(I )=S [1,4,7,9] _S [2,5,8,10] _S [3,6] .…”

mentioning

confidence: 99%

Bitableaux Bases for the Diagonally Invariant Polynomial Quotient Rings

Allen

1997

Advances in Mathematics

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“…Outside of invariant theory, the bitableau basis appears often in papers treating problems in representation theory and quantum groups. (See, e.g., [1], [32].) Let T , U be column-strict tableaux of the same shape and having k columns, and recall the submatrix notation (2.3).…”

Section: A Multigrading Of C[x] and Two Basesmentioning

confidence: 99%

Bitableaux and Zero Sets of Dual Canonical Basis Elements

Rhoades

Skandera

2011

Ann. Comb.

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Abstract. We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of C[x 1,1 , . . . , x n,n ]. As an application, we show that this basis is related by a unitriangular transition matrix to the simpler bitableau basis popularized by Désarménien-Kung-Rota. It follows that spaces spanned by certain subsets of the dual canonical basis can be characterized in terms of products of matrix minors, or in terms of their common zero sets.

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“…For example, if &=(4, 2, 1) then the Ferrers diagram of shape (4,3,2) where each cell contains its coordinate as its entry would be If &=(1 q ), the requirement that |Q m, k, & | =n implies that we may assume that q=m(n&1)+k. Similarly, if &=( p) then we may assume that p=m(n&1)+k.…”

Section: Introductionmentioning

confidence: 98%