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Longer titles found: Length of a Weyl group element (view)

searching for Weyl group 44 found (201 total)

alternate case: weyl group

5 21 honeycomb (801 words) [view diff] exact match in snippet view article find links to article

its symmetry group (the affine E ~ 8 {\displaystyle {\tilde {E}}_{8}} Weyl group) acts transitively on the k-faces for k ≤ 6. All of the k-faces for k

Double affine Hecke algebra (188 words) [view diff] exact match in snippet view article find links to article

Cherednik algebra, is an algebra containing the Hecke algebra of an affine Weyl group, given as the quotient of the group ring of a double affine braid group

Dual representation (1,699 words) [view diff] exact match in snippet view article find links to article

should happen that operator − I {\displaystyle -I} is an element of the Weyl group, then the weights of every representation are automatically invariant

Double affine braid group (138 words) [view diff] exact match in snippet view article find links to article

affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double affine Hecke algebras

Iwahori subgroup (800 words) [view diff] exact match in snippet view article find links to article

field has a Tits system (B,N), where B is a parahoric group, and the Weyl group of the Tits system is an affine Coxeter group. More precisely, Iwahori

Orthogonal group (7,820 words) [view diff] exact match in snippet view article find links to article

Weyl group of SO(2n) is represented in SO(2n) by the preimages under the standard injection SO(2n) → SO(2n + 1) of the representatives for the Weyl group

238 (number) (249 words) [view diff] exact match in snippet view article

2010). "Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits" (PDF). Journal of Physics A: Mathematical and Theoretical. 43

Gunter Malle (642 words) [view diff] exact match in snippet view article find links to article

was the question of whether every finite complex reflection group is a Weyl group of an object analogous to a finite group of Lie type. They baptized the

Pi (letter) (847 words) [view diff] exact match in snippet view article

(probably to better distinguish from elements w {\displaystyle w} of the Weyl group, than the usual notation ω {\displaystyle \omega } ). The lemniscate constant

Painlevé transcendents (2,778 words) [view diff] exact match in snippet view article find links to article

dihedral group of Bäcklund transformations (which is in fact the affine Weyl group of A 1 {\displaystyle A_{1}} ; see below). If b = 1 / 2 {\displaystyle

Kostant partition function (1,711 words) [view diff] exact match in snippet view article find links to article

nominally over the whole Weyl group, in most cases, the number of nonzero terms is smaller than the order of the Weyl group. Tarski, Jan; University of

900 (number) (3,815 words) [view diff] exact match in snippet view article

Finland 952 = 23 × 7 × 17, number of reduced words of length 3 in the Weyl group D_17, number of regions in regular tetradecagon with all diagonals drawn

List of ETH Zurich people (1,220 words) [view diff] exact match in snippet view article find links to article

Hermann Weyl, mathematician (Professor at the ETH) Known for: Einstein-Weyl group (Quantum Field Theory) Wendelin Werner, mathematician (Professor at the

Daya-Nand Verma (203 words) [view diff] case mismatch in snippet view article find links to article

Verma, Daya-Nand (1971), Mobius inversion for the Bruhat ordering on a Weyl Group, Ann. Sci. Ecole Norm. Sup. 4e Serie, t.4, pp. 393–398. J.E.Humphreys

N = 2 superconformal algebra (2,295 words) [view diff] exact match in snippet view article find links to article

(Ramond) The supercharge operator commutes with the action of the affine Weyl group and the physical states lie in a single orbit of this group, a fact which

Representation ring (849 words) [view diff] exact match in snippet view article find links to article

consisting of those class functions that are invariant under the action of the Weyl group (Atiyah and Hirzebruch, 1961). For the general compact Lie group, see

Dual snub 24-cell (651 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T'} 24-cells as quaternion orbit weights of D4 under the Weyl group W(D4): O(0100) : T = {±1,±e1,±e2,±e3,(±1±e1±e2±e3)/2} O(1000) : V1 O(0010) :

Blattner's conjecture (890 words) [view diff] exact match in snippet view article find links to article

vector can be written as a sum of non-compact positive roots WK is the Weyl group of K ρc is half the sum of the compact roots ρn is half the sum of the

Golden–Thompson inequality (988 words) [view diff] exact match in snippet view article find links to article

1103/PhysRev.137.B1127, MR 0189691 Kostant, Bertram (1973), "On convexity, the Weyl group and the Iwasawa decomposition", Annales Scientifiques de l'École Normale

E9 honeycomb (804 words) [view diff] exact match in snippet view article find links to article

is highly regular in the sense that its symmetry group (the affine E9 Weyl group) acts transitively on the k-faces for k ≤ 7. All of the k-faces for k

Bertram Kostant (1,209 words) [view diff] exact match in snippet view article find links to article

2307/2373470. JSTOR 2373470. Kostant, Bertram (1973). "On convexity, the Weyl group and the Iwasawa decomposition". Annales Scientifiques de l'École Normale

Yan Soibelman (221 words) [view diff] exact match in snippet view article find links to article

representation theory and symplectic geometry. He introduced the notion of quantum Weyl group, studied representation theory of the algebras of functions on compact

Affine root system (982 words) [view diff] exact match in snippet view article find links to article

given in the table is the number of orbits of simple roots under the Weyl group. In the Dynkin diagrams, the non-reduced simple roots α (with 2α a root)

Kyoji Saito (634 words) [view diff] exact match in snippet view article find links to article

general weight system: relations with singularity theory, the generalized Weyl group and its invariant theory, etc., in Katsumi Nomizu Selected papers on harmonic

Kac–Moody algebra (2,467 words) [view diff] exact match in snippet view article find links to article

(2010). "Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits". J. Phys. A: Math. Theor. 43 (15): 155–209. arXiv:1003.0564. Bibcode:2010JPhA

Weight (representation theory) (3,258 words) [view diff] exact match in snippet view article

is convenient to choose an inner product that is invariant under the Weyl group, that is, under reflections about the hyperplanes orthogonal to the roots

Nolan Wallach (1,055 words) [view diff] exact match in snippet view article find links to article

1–21 Invariant differential operators on a reductive Lie algebra and Weyl group representations, J. Amer. Math. Soc., vol. 6, no. 4, 1993, pp. 779–816

Weight (representation theory) (3,258 words) [view diff] exact match in snippet view article

is convenient to choose an inner product that is invariant under the Weyl group, that is, under reflections about the hyperplanes orthogonal to the roots

Affine symmetric group (10,249 words) [view diff] exact match in snippet view article find links to article

1112/S0010437X13007240, S2CID 16108179 Lam, Thomas (2015), "The shape of a random affine Weyl group element and random core partitions", Ann. Probab., 43 (4): 1643–1662,

't Hooft loop (1,925 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Lambda _{w}^{G}/W} lattice where W {\displaystyle W} is the Weyl group. The Lie algebra valued charge of the 't Hooft line can always be written

Alexander Varchenko (2,017 words) [view diff] exact match in snippet view article find links to article

with the symmetric group S n + 1 {\displaystyle S_{n+1}} which is the Weyl group of the simple Lie algebra of type A n {\displaystyle A_{n}} . In 1971

Siteswap (4,019 words) [view diff] exact match in snippet view article find links to article

viewed as certain elements of the affine symmetric group (the affine Weyl group of type A ~ n {\displaystyle {\tilde {A}}_{n}} ). One presentation of

K3 surface (5,241 words) [view diff] exact match in snippet view article find links to article

determines the automorphism group of X up to commensurability. Namely, let the Weyl group W be the subgroup of the orthogonal group O(Pic(X)) generated by reflections

Smith–Minkowski–Siegel mass formula (2,801 words) [view diff] exact match in snippet view article find links to article

lattice of dimension 8, the E8 lattice, whose automorphism group is the Weyl group of E8 of order 696729600, so this verifies the mass formula in this case

Quantum dilogarithm (801 words) [view diff] exact match in snippet view article find links to article

Models". arXiv:hep-th/9408041. Faddeev, L. D. (1995). "Discrete Heisenberg-Weyl group and modular group". Letters in Mathematical Physics. 34 (3): 249–254.

SIC-POVM (3,522 words) [view diff] exact match in snippet view article find links to article

T q {\displaystyle W(p,q)=S^{p}T^{q}} which generates the Heisenberg-Weyl group. This is a unitary operator since W ( p , q ) W † ( p , q ) = S p T q

Uniform 4-polytope (4,310 words) [view diff] exact match in snippet view article find links to article

Weyl group Conway Quaternion Abstract structure Order Coxeter diagram Coxeter notation Commutator subgroup Coxeter number (h) Mirrors m=2h Irreducible

3-transposition group (3,468 words) [view diff] exact match in snippet view article find links to article

3-transposition groups except W(D2)=22, with groups on Fischer's list (W stands for Weyl group). S 5 = O 4 − ( 2 ) {\displaystyle S_{5}=O_{4}^{-}(2)} has order 120,

Phase-space wavefunctions (2,161 words) [view diff] exact match in snippet view article find links to article

with the totality of coherent-state representations for the Heisenberg–Weyl group. The Wigner quasiamplitude, ψ {\displaystyle \psi } , and Torres-Vega–Frederick

Point groups in four dimensions (3,589 words) [view diff] exact match in snippet view article find links to article

Weyl group Conway Quaternion Abstract structure Coxeter diagram Coxeter notation Order Commutator subgroup Coxeter number (h) Mirrors (m) Full polychoric

Symmetric cone (16,607 words) [view diff] exact match in snippet view article find links to article

0. Given a frame (ei) in a Euclidean Jordan algebra E, the restricted Weyl group can be identified with the group of operators on ⊕ R ei arising from elements

Glossary of representation theory (5,008 words) [view diff] exact match in snippet view article find links to article

_{T}f(t)u(t)dt.} (Explicitly, u {\displaystyle u} is 1 over the cardinality of the Weyl group times the product of | e α ( t ) − e − α ( t ) | 2 {\displaystyle |e^{\alpha

Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article

{\mathfrak {g}}} . The transformation j(z) = −z−1 corresponding to the Weyl group element J induces the involutive automorphism σ given by σ ( a , T , b

Ethics of circumcision (6,570 words) [view diff] case mismatch in snippet view article find links to article

Bump D, Friedberg S (2011-07-25). "Statement E Implies Statement D". Weyl Group Multiple Dirichlet Series. Princeton University Press. doi:10