Geodesic
Harmonic analysis on semisimple Hopf algebras
Algebra i analiz, Tome 12 (2000) no. 5, pp. 3-27.

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Let $H$ be a semisimple Hopf algebra. The relationship is studied between the character algebra of $H$ and that of a Hopf subalgebra. Hecke algebras are discussed, as well as their links with quantum spaces of double cosets. An explicit expression for spherical functions is given. Also, Gelfand pairs are studied, and a description of Fourier analysis on symmetric spaces via spherical functions is presented. It is shown that the pair $(D(H), H)$ is a Gelfand pair if and only if $H$ is almost cocommutative; here $D(H)$ is the Drinfeld double of $H$.
Keywords: Coalgebra, quantum groups, Kac algebras, Gelfand pairs, Drinfeld double. 
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     author = {N. Andruskiewitsch and S. Natale},
     title = {Harmonic analysis on semisimple {Hopf} algebras},
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     number = {5},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2000_12_5_a0/}
}
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N. Andruskiewitsch; S. Natale. Harmonic analysis on semisimple Hopf algebras. Algebra i analiz, Tome 12 (2000) no. 5, pp. 3-27. http://geodesic.mathdoc.fr/item/AA_2000_12_5_a0/