The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
نویسندگان
چکیده
منابع مشابه
Generalized triangle inequalities and their applications
We present a survey of our recent work on generalized triangle inequalities in infinitesimal symmetric spaces, nonpositively curved symmetric spaces and Euclidean buildings. We also explain how these results can be used to analyze some basic problems of algebraic group theory including the problem of decomposition of tensor products of irreducible representations of complex reductive Lie groups...
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We compute the generalized triangle inequalities explicitly for all rank 3 symmetric spaces of noncompact type. For SL(4,C) there are 50 inequalities none of them redundant by [KTW]. For both Sp(6,C) and Spin(7,C) there are 135 inequalities of which 24 are trivially redundant in the sense that they follow from the inequalities defining the Weyl chamber ∆. There are 9 more redundant inequalities...
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A brief scan through the problem columns of various mathematical journals shows a continual outpouring of proposed problems involving what can be roughly described as “triangle inequalities”. A few examples will suffice to indicate the flavor of these perennial favorites: Let the sides of a triangle be a, b, c and let the angles be A, B, C. Let r and R be the inradius and circumradius, respecti...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2008
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0896