On uniqueness of branching to fixed point Lie subalgebras
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Santosh Nadimpalli
Abstract
Let
In many cases, we show that
Acknowledgements
We would like to thank C. S. Rajan for his comments on this work and his encouragement. We would like to thank R. Venkatesh for some discussions. We also thank the anonymous referee for many valuable comments.
References
[1] N. Bourbaki, Éléments de mathématique. Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées, Act. Sci. Indust. 1364, Hermann, Paris, 1975. Search in Google Scholar
[2] J. Bandlow, A. Schilling and N. M. Thiéry, On the uniqueness of promotion operators on tensor products of type A crystals, J. Algebraic Combin. 31 (2010), no. 2, 217–251. 10.1007/s10801-009-0182-3Search in Google Scholar
[3] C. Bowman and R. Paget, The uniqueness of plethystic factorisation, Trans. Amer. Math. Soc. 373 (2020), no. 3, 1653–1666. 10.1090/tran/8021Search in Google Scholar
[4] T. Gerber, J. Guilhot and C. Lecouvey, Generalised howe dualityand injectivity of induction: The symplectic case, preprint (2021), https://arxiv.org/abs/2110.04029. 10.5070/C62257878Search in Google Scholar
[5] J. Guilhot and C. Lecouvey, Isomorphic induced modules and Dynkin diagram automorphisms of semisimple Lie algebras, Glasg. Math. J. 58 (2016), no. 1, 187–203. 10.1017/S0017089515000142Search in Google Scholar
[6] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Grad. Texts in Math. 9, Springer, New York, 1972. 10.1007/978-1-4612-6398-2Search in Google Scholar
[7] V. G. Kac, Infinite-Dimensional Lie algebras, 3rd ed., Cambridge University, Cambridge, 1990. 10.1017/CBO9780511626234Search in Google Scholar
[8] K. Purbhoo and S. van Willigenburg, On tensor products of polynomial representations, Canad. Math. Bull. 51 (2008), no. 4, 584–592. 10.4153/CMB-2008-058-xSearch in Google Scholar
[9] C. S. Rajan, Unique decomposition of tensor products of irreducible representations of simple algebraic groups, Ann. of Math. (2) 160 (2004), no. 2, 683–704. 10.4007/annals.2004.160.683Search in Google Scholar
[10] R. Venkatesh and Sankaran Viswanath, Unique factorization of tensor products for Kac–Moody algebras, Adv. Math. 231 (2012), no. 6, 3162–3171. 10.1016/j.aim.2012.08.014Search in Google Scholar
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- The Singer transfer for infinite real projective space
- The Stiefel–Whitney classes of moment-angle manifolds are trivial
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- Construction of a class of spectral measures
- On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms
- Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood–Paley function characterizations
- Conway invariant Jacobi forms on the Leech lattice
- Geometric characterizations of Gromov hyperbolic Hölder domains
- Improved quantitative unique continuation for complex-valued drift equations in the plane
- On uniqueness of branching to fixed point Lie subalgebras
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Articles in the same Issue
- Frontmatter
- Wong–Zakai approximations and support theorems for stochastic McKean–Vlasov equations
- The Singer transfer for infinite real projective space
- The Stiefel–Whitney classes of moment-angle manifolds are trivial
-
On almost p-rational characters of
- Homogeneous four-manifolds with half-harmonic Weyl curvature tensor
- Construction of a class of spectral measures
- On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms
- Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood–Paley function characterizations
- Conway invariant Jacobi forms on the Leech lattice
- Geometric characterizations of Gromov hyperbolic Hölder domains
- Improved quantitative unique continuation for complex-valued drift equations in the plane
- On uniqueness of branching to fixed point Lie subalgebras
- Fefferman type criterion on weighted bi-parameter local Hardy spaces and boundedness of bi-parameter pseudodifferential operators
