Infinite-Dimensional Lie Algebras

By M. Wakimoto. 2000

748 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d9f11da0c657cf30f2f8b1e80c82094f168b340b

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In Algebra and Number Theory

Citations in the corpus

An algebraic approach to logarithmic conformal field theory (2001, background): “50) Under the S transformation, S : τ 7→ −1/τ , the θm,k functions transform as [58]”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, background): “(For more details concerning the connection with the dual root system of the affine root system Φ̂ see [24], Chapter 6.”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “…Göllnitz, and Slater [8] [102] [101] [195] to name a few), and the pursuit of further identities and their interpretations remains an active area of research largely due to applications in combinatorics, Lie theory, number theory and physics (for example, see [13], [129] and [145] to name a few).”
Representation theory of symmetric groups and related Hecke algebras (2009, neutral): “Following [105], let (h,Π,Π) be a realization of the Cartan matrix (aij)i,j∈I , so we have the simple roots {αi | i ∈ I}, the fundamental dominant weights”
Arithmetic invariants of discrete Langlands parameters (2010, methodology): “We invoke Kac’s classification [26] of torsion automorphisms of g, considering only those F ∈ Aut(g) for which g is semisimple (see also [40]).”
Hecke‐type double sums, Appell–Lerch sums, and mock theta functions, I (2012, background): “Our formula also proves the Hecke-type double sum identities found in Polishchuk [27] and Kac and Peterson [20].”
Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center (2005, background): “(2) R p−1 is the SL(2, Z)-representation realized in the sℓ(2) p−2 minimal model [28] [29].”
Finite quantum groups over abelian groups of prime exponent (2000, methodology): “Then(aij) is a generalized Cartan matrix [20].”
Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram (2001, methodology): “It is well known, see for example Exercise 14.26 in [ 11 ], that the matrix coefficient of the operators ± are the skew Schur functions, namely”
Positivity and canonical bases in rank 2 cluster algebras of finite and affine types (2003, methodology): “According to [13], the set of imaginary roots can be defined as follows: (3.”