By Steinberg’s tensor product Theorem, for any dominant weight λ we have an isomorphismL(λ) = L(λ′) L(λ′′)F, where F is the Frobenius morphism. ... the natural representation and depending on whether λ′′i and λ′′j are related by a
Most of the work here involves a series oflemmas concerning polar spaces, which forms a natural extension and completion of the analysisin [16]. ... 9. In light of Corollary 1.14 it is natural that the theory of domesticity in rank 2 buildings
in addition to the decomposition of thetensor product of two highest weight representations. ... We denote by α = 2α/〈α, α〉 the coroot associated toα Φ with respect to the inner product 〈, 〉 : hh C.
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in addition to the decomposition of thetensor product of two highest weight representations. ... We denote by α = 2α/〈α, α〉 the coroot associated toα Φ with respect to the inner product 〈, 〉 : hh C.
Since W affJ acts transitively onAJ , and since AJ AJ , there is w W affJ such that wA = AJ (and in particular, wλ AJ).Since w is a product of reflections ... 17. There is a natural action of TJ on J-folded alcove paths, as follows (recall the
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theorem “descends” to give an inner product on Lusztig’s asymptotic algebra J. ... To each right cell Υ of W there is a natural right H-module HΥ constructed as follows.
In PDEs with translational symmetry in a d-dimensionalphysical space, the skew product reduces to. ... Evaluating the projections (17)–(18) determines the drift coefficients, and the evolution equationfor the collective coordinates becomes the