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math.RT2012
Rank 2 symmetric hyperbolic Kac-Moody algebras and Hilbert modular forms
Henry H. Kim, Kyu-Hwan Lee
In this paper we study rank two symmetric hyperbolic Kac-Moody algebras H(a) and their automorphic correction in terms of Hilbert modular forms. We associate a family of H(a)'s to…
math.RT2011
Quantum affine algebras, canonical bases and -deformation of arithmetical functions
Henry H. Kim, Kyu-Hwan Lee
In this paper, we obtain affine analogues of Gindikin-Karpelevich formula and Casselman-Shalika formula as sums over Kashiwara-Lusztig's canonical bases. Suggested by these formula…