Results 1 to 10 of about 2,902 (161)
Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]
Nature CommunicationsVariational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Enrico Fontana +7 more
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A representation for an adjoint operator
Journal of Numerical Analysis and Approximation Theory, 1975 Not available.
Stephen P. Travis
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Torus knots in adjoint representation and Vogel’s universality
European Physical Journal C: Particles and FieldsVogel’s universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $$\alpha ,\beta ,\gamma $$ α , β , γ , which are homogeneous coordinates of Vogel’s plane.
Liudmila Bishler, Andrei Mironov
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Decomposition of the Adjoint Representation of the Small Quantum sl 2 [PDF]
Communications in Mathematical Physics, 1997 Given a finite type root datum and a primitive root of unity $q=\sqrt[l]{1}$, G.~Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra $\fu$ over the cyclotomic field ${\Bbb Q}(\sqrt[l]{1})$. In this note we study the adjoint representation $\ad$ of $\fu$ in the simplest case of the root datum $sl_2$.
exaly +3 more sources
A Rankin-Selberg integral for the adjoint representation of GL3
Inventiones Mathematicae, 1991 This paper deals with some problems towards the analytic continuation and functional equation of the \(L\)-function \(L(s,\pi,r)\) attached to a cuspidal representation of \(GL_ 3\) and the eight dimensional adjoint representation \(r\) of the \(L\)-group \(GL_ 3(\mathbb{C})\) of \(GL_ 3\). The Basic Identity is established for the global zeta-integral;
David Ginzburg, Ginzburg David
exaly +2 more sources
On the adjoint representation of a hopf algebra [PDF]
Proceedings of the Edinburgh Mathematical Society, 2020 AbstractWe consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{{\textrm ad\,fin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as module over a cocommutative Hopf subalgebra), we show that $H_{{\textrm ad\,fin}}$ is a ...
Kolb S, Lorenz M, Nguyen B, Yammine R
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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Worldline description of a bi-adjoint scalar and the zeroth copy
Journal of High Energy Physics, 2021 Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective.
Fiorenzo Bastianelli +2 more
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GMOR relation for a QCD-like theory from S-duality
Physics Letters B, 2022 Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an O3 plane and N D3 anti-branes and it realises a USp(2N) ‘electric’ gauge theory with four “quarks” in the two-index ...
Adi Armoni, Henry Harper-Gardner
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An adjoint representation for polynomial algebras [PDF]
Proceedings of the American Mathematical Society, 1987 This paper shows that a graded polynomial algebra over F 2 {F_2}
Mitchell, Stephen A., Stong, Robert E.
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