Multiplicity of the Adjoint Representation in Simple Quotients of the Enveloping Algebra of a Simple Lie Algebra [PDF]
Transactions of the American Mathematical Society, 1989 Let g \mathfrak {g} be a complex simple Lie algebra, h \mathfrak {h} a Cartan subalgebra and U ( g ) U(\mathfrak {g}) the enveloping algebra of g \mathfrak {g} . We calculate for each maximal two-sided
Anthony D. Joseph
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The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
Advances in Mathematics, 2015 Final version. More misprints corrected.
Corrado De Concini +2 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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Homology of the Lie algebra of vector fields on the line with coefficients in symmetric powers of its adjoint representation [PDF]
Functional Analysis and Its Applications, 2006 We compute the homology of the Lie algebra~$W_1$ of (polynomial)vector fields on a line with coefficients in symmetric powersof its adjoint representation. We also list the results obtained so farfor the homology with coefficients in tensor powers and, in turn, use themfor partially computing the homology of the Liealgebra of currents on a line with ...
Vladimir Dotsenko
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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
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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
, 2014 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.
Pamela E. Harris +2 more
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, 2023 This paper exhibits fundamental structure underlying Lie algebra homology with coefficients in tensor products of the adjoint representation, mostly focusing upon the case of free Lie algebras. The main result yields a DG category that is constructed from the PROP associated to the Lie operad.
Geoffrey Powell
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, 2004 The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra structure. Such a description is rather imprecise: these dimensions may coincide for cohomology spaces of distinct ...
Alexei Lebedev +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 ...
C. Concini +3 more
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