“…Chazy considered also the equation 000 6 00 + 9 0 2 + 432 n 2 36 0 1 2 2 2 = 0 ( C: 41) for an integer n > 6. The correspondent Lame equation y 00 m(m + 1 ) } 0 ( x ) y = 0 ( C:42) has m = 3 n 1 2 : (C:43)…”
Abstract. These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological eld theories.
“…Chazy considered also the equation 000 6 00 + 9 0 2 + 432 n 2 36 0 1 2 2 2 = 0 ( C: 41) for an integer n > 6. The correspondent Lame equation y 00 m(m + 1 ) } 0 ( x ) y = 0 ( C:42) has m = 3 n 1 2 : (C:43)…”
Abstract. These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological eld theories.
It is proved that general consistency requirements of stability under complex analytic change of charts show that primary currents in finite chiral W-algebras are described in terms of pure gravitational variables. 1998 PACS Classification: 11.10 -11.25 hf
“…This coadjoint action is Hamiltonian and has a moment map µ : ( g ′ ) * → n + [z, z −1 ] * = n − [z, z −1 ], where n − is the opposite nilpotent subalgebra in g, and we have identified the space n + [z, z −1 ] * with n − [z, z −1 ] using the standard scalar product on g ′ . The reduced space entering the definition of the algebra W (g) corresponds to the value f of the moment map µ, where f is a regular nilpotent element in n − ⊂ n − [z, z −1 ] regarded as a Lie subalgebra in g. The reduction procedure described above was introduced in [14] and is called now the Drinfeld-Sokolov reduction procedure.…”
Abstract. We define deformations of W-algebras associated to complex semisimple Lie algebras by means of quantum Drinfeld-Sokolov reduction procedure for affine quantum groups. We also introduce Wakimoto modules for arbitrary affine quantum groups and construct free field resolutions and screening operators for the deformed W-algebras. We compare our results with earlier definitions of q-W-algebras and of the deformed screening operators due to Awata, Kubo, Odake, Shiraishi [60,6,7], Feigin, E. Frenkel [22] and E. Frenkel, Reshetikhin [34]. The screening operator and the free field resolution for the deformed W-algebra associated to the simple Lie algebra sl 2 coincide with those for the deformed Virasoro algebra introduced in [60].
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