Root systems and orthogonal groups of root lattices
نویسندگان
چکیده
منابع مشابه
cellular behavior and scanning electron microscope evaluation of pro-root mta, root mta and modified mta on fibroblast l929
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15 صفحه اولRoot Systems and Coxeter Groups
This is a brief review of root systems and Coxeter groups, intended as background material for a course on double affine Hecke algebras and Macdonald polynomials. They are still incomplete in places. 1. Root systems Much of this material can be found in [Bou]. Let V be a real vector space with a positive definite inner product 〈·, ·〉. If α ∈ V is a non-zero vector, define the reflection sα in t...
متن کاملRoot Lattices and Quasicrystals
It is shown how root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All non-periodic symmetries observed so far are covered in minimal embedding with maximal symmetry. For the construction of quasiperiodic tiling models by means of projection from higherdimensional periodic structures, the primitive hypercubic lattices are...
متن کاملOrthogonal Polynomials Associated with Root Systems
Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W , such that S (but not necessarily R) is reduced. For each such pair (R, S) we construct a family of W -invariant orthogonal polynomials in several variables, whose coefficients are rational functions of parameters q, t1, t2, . . . , tr, where r (= 1, 2 or 3) is the number of W -orbits in...
متن کاملThe Root Lattices of the Complex Reeection Groups
Four questions on the classiication of root lattices, root systems and bad primes of the nite irreducible complex reeection groups raised in a letter by Brou e are fully answered.
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1984
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381757735