Results 11 to 20 of about 57,089 (167)
The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula
, 2013 Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula is factorial in the rank of the Lie algebra and the value of the partition function is unknown.
Harris, Pamela E. +2 more
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On the geometry underlying a real Lie algebra representation [PDF]
, 2012 Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $\pi$ of $G$, one obtains by differentiation a representation $d\pi$ of $\mathfrak g$ by unbounded, skew-adjoint operators.
Le-Bert, Rodrigo Vargas
core +2 more sources
Experimental Mathematicsv4 further improvements to the exposition; 19 pages. (v3 minor revision together with addition of an Appendix; 17 pages. v2 Very minor revision. 14 pages.)
Geoffrey Powell
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Characterizing barren plateaus in quantum ansätze with the adjoint representation. [PDF]
Nat Commun, 2023 Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Fontana E +7 more
europepmc +3 more sources
Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation [PDF]
Journal of Mathematics and Physics, 2018 In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation.
Yuwang Hu, Jiefeng Liu, Y. Sheng
semanticscholar +1 more source
The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
, 2013 For a simple complex Lie algebra g we study the space of invariants A = ( ⋀ g ⁎ ⊗ g ⁎ ) g , which describes the isotypic component of type g in ⋀ g ⁎ , as a module over the algebra of invariants ( ⋀ g ⁎ ) g .
C. Concini, P. Papi, C. Procesi
semanticscholar +1 more source
The Adjoint Braid Arrangement as a Combinatorial Lie Algebra via the Steinmann Relations [PDF]
Journal of Pure and Applied Algebra, 2019 We study the dual action of Lie elements on faces of the adjoint braid arrangement, interpreted as the discrete differentiation of functions on faces across hyperplanes.
Zhengwei Liu +2 more
semanticscholar +1 more source
A Representation of Weyl-Heisenberg Lie Algebra in the Quaternionic Setting [PDF]
, 2017 Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart.
B. Muraleetharan +2 more
semanticscholar +1 more source
Entropy, 2016 We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
doaj +1 more source
Journal of High Energy Physics, 2018 We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module.
Martin Cederwall, Jakob Palmkvist
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