Results 11 to 20 of about 154 (92)
An Algorithm for the Second Immanant [PDF]
Mathematics of Computation, 1984 Let χ \chi be an irreducible character
Grone, Robert, Merris, Russell
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, 2023 We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional character $\chi$, we
Bolognini, Davide, Sentinelli, Paolo
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Webs and canonical bases in degree two [PDF]
, 2023 We show that Lusztig's canonical basis for the degree two part of the Grassmannian coordinate ring is given by SL(k) web diagrams. Equivalently, we show that every SL(2) web immanant of a plabic graph for Gr(k,n) is an SL(k) web invariant.Comment ...
Fraser, Chris
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A full complexity dichotomy for immanant families [PDF]
, 2021 Given an integer n ≥ 1 and an irreducible character χλ of Sn for some partition λ of n, the immanant immλ:ℂn× n→ℂ maps matrices A∈ℂn× n to immλ(A)=∑π∈ Snχλ(π)∏i=1nAi,π(i).
Curticapean, Radu-Cristian +1 more
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Hook-Shape Immanant Characters from Stanley-Stembridge Characters [PDF]
, 2023 We consider the Schur-positivity of monomial immanants of Jacobi-Trudi matrices, in particular whether a non-negative coefficient of the trivial Schur function implies non-negative coefficients for other Schur functions in said immanants.
Lesnevich, Nathan R. T.
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On the dual canonical and Kazhdan–Lusztig bases and 3412-, 4231-avoiding permutations [PDF]
, 2008 Using Du’s characterization of the dual canonical basis of the coordinate ring O(GL(n,C)), we express all elements of this basis in terms of immanants. We then give a new factorization of permutations w avoiding the patterns 3412 and 4231, which in turn ...
Skandera, Mark
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From Cauchy's determinant formula to bosonic and fermionic immanant identities [PDF]
, 2023 Cauchy's determinant formula (1841) involving $\det ((1-u_i v_j)^{-1})$ is a fundamental result in symmetric function theory. It has been extended in several directions, including a determinantal extension by Frobenius [J. reine angew. Math.
Khare, Apoorva, Sahi, Siddhartha
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On immanants of Jacobi-Trudi matrices and permutations with restricted position [PDF]
, 1993 Let [chi] be a character of the symmetric group Ln. The immanant of an n x n matrix A = [aij] with respect to [chi] is [Sigma]w [epsilon] Sn [chi](w) a1,w(1) ... an,w(n).
Stanley, Richard P. +3 more
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Oppenheim's Inequality for the Second Immanant
, 1987 Denote by d2 the immanant afforded by Sn and the character corresponding to the partition (2, 1n-2). If n ≥ 4, the following analog of Oppenheim's inequality is proved:for all n-by-n positive semidefinite hermitian A and B.
Russell Merris
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Linear preservers of immanants on symmetric matrices [PDF]
, 1997 Let F be an arbitrary subfield of the complex numbers, and let Hn(F) be the space of the n × n symmetric matrices with entries in F. We describe the linear operators of Hn(F) that preserve an immanant dχ, where χ is an irreducible nonlinear character of ...
Purificação^Coelho, M. +1 more
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