TY - JOUR
T1 - Algebraic classical W-algebras and Frobenius manifolds
AU - Dinar, Yassir Ibrahim
N1 - Funding Information:
The author thanks Boris Dubrovin for posting him this problem and for encouragement, support and useful discussions. The author also thanks Di Yang for stimulating discussions and anonymous reviewers whose comments/suggestions helped improve and clarify this article. A part of this work was done during the author visits to the Abdus Salam International Centre for Theoretical Physics (ICTP) and the International School for Advanced Studies (SISSA) through the years 2014-2017. This work was also funded by the internal grant of Sultan Qaboos University (IG/SCI/DOMS/15/04).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2021/10
Y1 - 2021/10
N2 - We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.
AB - We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which forms an exact Poisson pencil, defines an algebraic classical W-algebra, admits a dispersionless limit, and its leading term defines an algebraic Frobenius manifold. This leads to a uniform construction of algebraic Frobenius manifolds corresponding to regular cuspidal conjugacy classes in irreducible Weyl groups.
KW - Classical W-algebra
KW - Common equilibrium points
KW - Drinfeld–Sokolov reduction
KW - Exact Poisson pencil
KW - Frobenius manifolds
KW - Nilpotent orbits in Lie algebras
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U2 - 10.1007/s11005-021-01458-2
DO - 10.1007/s11005-021-01458-2
M3 - Article
AN - SCOPUS:85114352935
SN - 0377-9017
VL - 111
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 5
M1 - 115
ER -