The classical groups

By Robert A. Wilson. 2009

1,027 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

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Citations in the corpus

The Ambient Metric (2007, background): “But in two dimensions, a trace-free tensor Aijk satisfying Aijk = Ai[jk] andA[ijk] = 0 must vanish identically (see [W]).”
Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments (2005, neutral): “(52) Now we apply Weyl’s formulas [25] χ[K](1) = k! ∏m i<j (ki − kj − i + j) Γm(m,K) (53) and3 χ{K}(Λ) = det ( λ kj+m−j i )”
Local random quantum circuits are approximate polynomial-designs: numerical results (2012, background): “Now, we can find, as a consequence of the SchurWeyl duality [35] that all operators X invariant under action of Pi,i+1 can be written as a sum of permutation operators Vπ,(i,i+1), permuting t copies of the Hilbert space H⊗t i,i+1.”
Free Lie algebroids and the space of paths (2007, background): “The following statement is one of the many instances of the “main theorem of invariant theory” [We].”
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities (2009, methodology): “We borrow the idea of the next statement from [40], [29], [2].”
The convolution operation on the spectra of algebras of symmetric analytic functions (2012, neutral): “[1,2]).”
The Brauer Category and Invariant Theory (2012, background): “Introduction The fundamental theorems [W] of classical invariant theory are concerned with generators and relations for invariants of classical group actions, and can be formulated in different ways [GW].”
Vacuum stability of a general scalar potential of a few fields (2016, background): “Orbits of φ are specified by invariant polynomials P (φ) [32, 33, 34].”
A minimal Set of Generators for the Ring of multisymmetric Functions (2007, background): “It is well known and often (falsely) attributed to Weyl [25] that when A is purely of characteristic 0 then ΓA(B) is generated by the pα’s (or the eα’s) with |α| 6 d.”
Dualities and Representations of Lie Superalgebras (2012, methodology): “The tensor FFT for classical groups can be found in Weyl [We].”
Group theoretical methods in machine learning (2008, methodology): “The generalization of Bochner’s theorem to locally compact Abelian groups was provided by Weil [1940], Povzner [1940] and Raikov [1940]. The irreducible representations of Abelian groups are one dimensional, hence in this case continuous characters and irreducible representations coincide.”
Non-commutative resolutions of quotient singularities for reductive groups (2015, neutral): “1 [64] The morphism S+ t,h → RH : yi j → yi j is an isomorphism.”
THE SECOND FUNDAMENTAL THEOREM OF INVARIANT THEORY FOR THE ORTHOGONAL GROUP (2011, background): “One formulation of the first fundamental theorem of invariant theory for O(V ) [21], [1] is as follows (see [15], [13], [17], [18], [19, Prop.”
Tame topology of arithmetic quotients and algebraicity of Hodge loci (2018, background): “By a classical result of Hilbert (see [W46, Ch. VIII, § 14]) the (graded 2.2.”