affine Kac-Moody algebra
Involutive automorphisms and real forms of Kac Moody algebras
... conjugacy classes of the involutive automorphisms within the group of all automorphisms of an untwisted complex affine Kac-Moody algebra.. The formulation in question enables all of the.[r] ...
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Root Multiplicities of the Indefinite Kac-Moody Lie Algebra HD_4^{(3)}
... a Kac-Moody algebra of affine or indefinite type, we say α is a real root if α is w-conjugate to a simple ...an affine Kac-Moody algebra g, then kα is also an ...
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Brown_unc_0153D_14830.pdf
... the Kac-Weyl character formula to write the multiplicity of a component as a complicated alternating sum of power ...the affine Kac-Moody algebra A (1) 1 , this is possible because ...
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Classification of Orbifold Modules under an Automorphism of Order Two.
... Lie algebra of finite type, the lattice vertex algebra gives a representation of the associated affine Kac-Moody algebra at level one (see Theorem ...
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Root System and Dynkin Diagrams for the General Class of Indefinite Quasi Affine Kac Moody Algebras QAG2(1)
... Quasi Affine (QA) type if S(A) has a proper connected sub diagram of affine type with n-1 ...the Kac-Moody algebra g(A) is of QA ...
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Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups
... the Kac- Moody algebra context, the generalised Cartan matrix entries are integers, as they appear as powers of the adjoint action in the Chevalley-Serre ...no Kac-Moody algebras exist, ...
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The Affine Lie Algebra s^ln(C) and its Z-algebra Representation.
... arrangement of creation and annihilation operators. Vertex operators were discovered as physi- cists delved into subjects like conformal field theory and string theory (cf. [13], [18]). Algebras of vertex operators were ...
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Root multiplicities of the indefinite type Kac-Moody algebras HC[subscript n]1
... a Kac-Moody algebra, g(A), of finite type the following statements are true: there exists an ω ∈ W such that ω(α) = α i for some i ∈ I, mult(α) = 1, and kα is a root if and only if k = ± ...of ...
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Vertex Representations for Yangians of Kac-Moody algebras
... of affine type [FrKa, MRY], the argument used to prove the above proposition for t associated to the Cartan matrix of an arbitrary simply laced Kac-Moody Lie algebra is the same, and analogous ...
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Crystals for Demazure Modules of Special Linear Quantum Affine Type
... minimal and t is then called the length of w. We let l(w) denote the length of w. If g is a Kac-Moody Lie algebra of finite type, then all of the roots are in the Weyl orbit of simple roots. In other ...
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Demazure Crystals for the Quantum Affine Algebra Uq(D4^(3)).
... Lie algebra while studying the geometric symmetries of differential ...Lie algebra, Wilhelm Killing and ´ Elie Cartan showed the necessity to classify all finite dimensional simple Lie ...Victor Kac ...
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Some Maximal Dominant Weights and Their Multiplicities for Affine Lie Algebra Representations.
... multiplicities can be studied using a combinatorial tool that comes out of studying quantum groups. Quantum groups (which are not actually groups), were introduced independently by Drinfel 0 d [2] and Jimbo [9] in 1985. ...
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On Demazure Crystals for the Quantum Affine Algebra U_q(sl^(n))
... A Demazure module is a certain finite-dimensional subspace of an integrable module for a Kac- Moody algebra parameterized by elements in the Weyl group and dominant integral weights. Kashi- wara ...
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The Hyperbolic Kac-Moody Lie Algebra of Type G_2^(1) and its Root Multiplicities.
... For Kac-Moody algebras of all types, the real roots are known to have multiplicity equal to ...type Kac-Moody algebras are real roots and thus have multiplicity equal to ...For affine ...
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Affine Kac Moody groups : bounded presentations and subgroup growth
... Lie algebra in positive ...Lie algebra and h ∨ was the dual Coxeter number) and it was necessary to show that the maximal dimension of the centraliser of a non-zero semisimple element was not greater than ...
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Braided Lie bialgebras associated to Kac Moody algebras
... Lie algebra situation to the infinite-dimensional Kac–Moody ...Lie algebra, the current algebra k[u] ⊗ g over a finite-dimensional simple Lie algebra ...of ...
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Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities
... of Kac-Moody ...finite, affine, and indefinite. Of the affine Lie algebras, the untwisted affine Lie algebras are the easiest to construct (a list of these untwisted affine GCMs ...
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Root Multiplicities of the Indefinite Type Kac-Moody Algebra HD_n^(1).
... Victor Kac ([15]) and Robert Moody ([33]) independently introduced a class of Lie algebras called Kac-Moody algebras, to generalize the concept of finite dimensional semisimple Lie algebras to ...
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On the Quasi Hyperbolic Kac Moody Algebra QHA7(2)
... level three and the structure of the components of the maximal ideals upto level four were determined by Uma Maheswari and Krishnaveni. For some quasi affine Kac Moody algebras QAC 2(1) , QAG 2(1) ...
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Presentations of Affine Kac Moody groups
... Let P be the weight lattice, Q the root lattice of the corresponding Kac–Moody Lie algebra. The weight lattice P is the root lattice X for a simply connected root datum. Mutatis mutandis, Q for an ...
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