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
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Euler’s difference table and the decomposition of tensor powers of the adjoint representation of the $$A_n$$ Lie algebra [PDF]
Theoretical and mathematical physics, 2022 By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
A. M. Perelomov
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The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
, 2015 For a simple complex Lie algebra $\mathfrak g$ we study the space of invariants $A=\left( \bigwedge \mathfrak g^*\otimes\mathfrak g^*\right)^{\mathfrak g}$, (which describes the isotypic component of type $\mathfrak g$ in $ \bigwedge \mathfrak g^*$) as a
De Concini, Corrado +2 more
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ...
Oksana Ye. Hentosh
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The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula [PDF]
, 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 ...
Pamela E. Harris +2 more
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On special covariants in the exterior algebra of a simple Lie algebra [PDF]
, 2014 We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ...
De Concini, Corrado +3 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
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The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
, 2013 Corrado De Concini +2 more
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Multiplicity of the adjoint representation in simple quotients of the enveloping algebra of a simple Lie algebra [PDF]
, 1989 Anthony Joseph
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