Compact Simple Lie Groups and Their C-, S-, and E-Transforms by Jiri Patera

Subjects: “…compact simple Lie groups…”
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Positive definite distributions on semi-simple Lie groups, by Barker, William Henry

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Local Second Order Sobolev Regularity for <i>p</i>-Laplacian Equation in Semi-Simple Lie Group by Chengwei Yu, Yue Zeng

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<title language="eng">K-theory for the C*-algebras of continuous functions on certain homogeneous spaces in semi-simple Lie groups by Takahiro Sudo

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Cubature Formulas of Multivariate Polynomials Arising from Symmetric Orbit Functions by Jiří Hrivnák, Lenka Motlochová, Jiří Patera

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Dual Pairs of Holomorphic Representations of Lie Groups from a Vector-Coherent-State Perspective by David J. Rowe, Joe Repka

Subjects: “…representations of simple Lie groups…”
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On Reidemeister torsion of flag manifolds of compact semisimple Lie groups by Cenap Özel, Habib Basbaydar, Yasar Sözen, Erol Yilmaz, Jung Rye Lee, Choonkil Park

“…In this paper we calculate Reidemeister torsion of flag manifold $K/T$ of compact semi-simple Lie group $K=SU_{n+1}$ using Reidemeister torsion formula and Schubert calculus, where $T$ is maximal torus of $K$. …”
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Highest weights, projective geometry, and the classical limit: I. Geometrical aspects and the classical limit by Hannabuss, K

“…This paper starts with a new proof that highest weight vectors for semi-simple Lie group representations can be characterised by quadratic equations, and finds the automorphism group of this quadratic variety. …”

Metric geometries over the split quaternions by Dancer, A, Jørgensen, H, Swann, A

“…These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. …”

Extended geometries by Martin Cederwall, Jakob Palmkvist

“…A universal form of the (pseudo-)action determines the dynamics in all cases without ancillary transformations, and also for a restricted set of cases based on the adjoint representation of a finite-dimensional simple Lie group. Our construction reproduces (the internal sector of) all previously considered cases of double and exceptional field theories.…”
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Adjoint orbits, generalised parallelisable spaces and consistent truncations by Louise Anderson

“…Abstract The aim of this note is to present some new explicit examples of O(d, d)generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits O $$ \mathcal{O} $$ of some semi-simple Lie group G. Using this construction, an explicit expression for a generalised frame is given in the case when the orbits are regular, but subtleties arise when they become degenerate. …”
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Subgroup growth of lattices in semisimple Lie groups by Lubotzky, A, Nikolov, N

“…In the most general case our results depend on the Generalized Riemann Hypothesis for number fields but we can state the following unconditional theorem: Let $G$ be a simple Lie group of real rank at least 2, different than $D_4(\bbc)$, and let $\Gamma$ be any non-uniform lattice of $G$. …”

Geometric Langlands correspondence near opers by Teleman, C, Frenkel, E

“… <p style="text-align:justify;"> Let G be a complex, connected semi-simple Lie group, L G its Langlands dual group, BunG the moduli stack of G-bundles on a smooth projective curve Sigma over C, LocLG the moduli stack of flat L G-bundles on Sigma. …”

Krein Spaces in de Sitter Quantum Theories by Ahmed Youssef, Petr Siegl, Jean-Pierre Gazeau

“…Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecomposable representation cohomology which deserves to be thoroughly studied in view of quantization of the corresponding carrier fields. …”
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The teleparallel complex by Martin Cederwall, Jakob Palmkvist

“…We illustrate with a derivation of teleparallel Ehlers geometry, where the extended coordinate module is the adjoint module of a finite-dimensional simple Lie group.…”
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Global anomalies in 8d supergravity by Yasunori Lee, Kazuya Yonekura

“…It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in 8d N $$ \mathcal{N} $$ = 1 supergravity theory, have anomalies. …”
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Ancient solutions of the homogenous Ricci flow on flag manifolds by S. Anastassiou, I. Chrysikos

“…For any flag manifold M=G/K of a compact simple Lie group G we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. …”
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Rank, combinatorial cost and homology torsion growth in higher rank lattices by Abert, M, Gelander, T, Nikolov, N

“…<br/>Most non-uniform lattices in higher rank simple Lie groups are right angled. We provide the first examples of uniform (co-compact) right angled arithmetic groups in SL(n, R), n ≥ 3 and SO(p, q) for some values of p, q. …”

Superuniversality of Superdiffusion by Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

“…For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group G, we find that finite-temperature transport of Noether charges associated with symmetry G in thermal states that are invariant under G is universally superdiffusive and characterized by the dynamical exponent z=3/2. …”
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Poisson-Lie duals of the η deformed symmetric space sigma model by Ben Hoare, Fiona K. Seibold

“…Abstract Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. …”
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