WebNov 14, 2009 · Also applications in the case where dimt = 1 are used in Borel–de Siebenthal theory to determine irreducibility theorems for certain equal rank subalgebras of g. In fact the irreducibility results readily yield a proof of the main assertions of the Borel–de Siebenthal theory. WebSep 1, 1984 · In fact the irreducibility results readily yield a proof of the main assertions of the Borel-de Siebenthal theory. View full-text. Article. The McKay correspondence, the Coxeter element and ...

On Borel–de Siebenthal Representations - Oxford Academic

WebBorel–de Siebenthal pairs, global Weyl modules... 651 is a free Aλ-module of finite rank. This fact is false for general λ and we give an example of this in Sect. 7. However, we … WebPage actions. Read; View source; History; ZWI Export; Group theory → Lie groups Lie groups liddell lowboy trailers

Borel–de Siebenthal theory - Wikipedia

WebIn mathematics, Borel–de Siebenthal theory describes the closed connected subgroups of a compact Lie group that have maximal rank, i.e. contain a maximal torus. It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the theory in 1949. Each such subgroup is the identity component of the centralizer of its … In mathematics, Borel–de Siebenthal theory describes the closed connected subgroups of a compact Lie group that have maximal rank, i.e. contain a maximal torus. It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the theory in 1949. Each such … See more Let G be connected compact Lie group with maximal torus T. Hopf showed that the centralizer of a torus S ⊆ T is a connected closed subgroup containing T, so of maximal rank. Indeed, if x is in CG(S), there is a maximal … See more A subset Δ1 ⊂ Δ is called a closed subsystem if whenever α and β lie in Δ1 with α + β in Δ, then α + β lies in Δ1. Two subsystems Δ1 and … See more The equal rank case with K non-semisimple corresponds exactly to the Hermitian symmetric spaces G / K of compact type. In fact the … See more Borel and de Siebenthal classified the maximal closed connected subgroups of maximal rank of a connected compact Lie group. The general classification of connected closed subgroups of maximal rank can be reduced to this … See more Let G be a connected compact semisimple Lie group, σ an automorphism of G of period 2 and G the fixed point subgroup of σ. Let K be a closed subgroup of G lying between G and its See more 1. ^ Helgason 1978 2. ^ Wolf 2010 3. ^ See: 4. ^ Wolf 2010 5. ^ Wolf 2010, p. 276 6. ^ See: See more Webif H / K is irreducible with K non-semisimple, the compact group H must be simple and K of maximal rank. From Borel-de Siebenthal theory, the involution σ is inner and K is the centralizer of its center, which is isomorphic to T.In particular K is connected. It follows that H / K is simply connected and there is a parabolic subgroup P in the complexification G … mclaren credit services