ガロア第一論文及びその関連の資料スレ

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357: １３２人目の素数さん [] 2023/02/12(日) 09:52:10.05 ID:t5GdbcIg

つづき

Moreover, the linear span of the functions χΛ(τ,0)
for Λ
of fixed level k
is invariant under the modular transformations

This turned out to be a key fact in the representation theory of affine algebras, as well as its applications to conformal field theory (see [Ve]), to 2
-dimensional lattice models [DaJiKuMiOk], and even to knot theory[YaGe].

References
[DaJiKaMi] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, "Transformation groups for soliton equations" M. Jimbo (ed.) T. Miwa (ed.), Proc. RIMS Symp., World Sci. (1983) pp. 39-120
[DaJiKuMiOk] E. Date, M. Jimbo, A. Kuniba, T. Miwa, M. Okado, "Exactly solvable SOS models" Nucl. Phys., B290 (1987) pp. 231-273 MR0910849 Zbl 0679.17010
[FrKa] I.B. Frenkel, V.G. Kac, "Basic representations of affine Lie algebras and dual resonance models" Invent. Math., 62 (1980) pp. 23-66 MR0595581 Zbl 0493.17010
[FrLeMe] I. Frenkel, J. Lepowsky, A. Meurman, "Vertex operator algebras and the Monster", Acad. Press (1989) MR1167718 MR0996026 Zbl 0674.17001
[GrScWi] M.B. Green, J.H. Schwarz, E. Witten, "Superstring theory", Cambridge Univ. Press (1987) MR0922731 MR0915347 MR0878144 MR0878143 Zbl 0637.53111 Zbl 0619.53002
[Ka] V.G. Kac, "Simple irreducible graded Lie algebras of finite growth" Math. USSR Izv., 2 (1968) pp. 1271-1311 Izv. Akad. Nauk USSR Ser. Mat., 32 (1968) pp. 1923-1967 MR0259961 Zbl 0222.17007
[Mo] R.V. Moody, "A new class of Lie algebras" J. of Algebra, 10 (1968) pp. 211-230 MR0229687 Zbl 0191.03005
[YaGe] C.N. Yang (ed.) M.L. Ge (ed.), Braid group, knot theory and statistical mechanics, World Sci. (1989) MR1062420 Zbl 0716.00010
(引用終り)
以上

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