Integrability plays a central role in solving many body problems in physics. The explicit construction of the Jack polynomials is an essential ingredient in solving the Calogero–Sutherland model, which is a one-dimen...Integrability plays a central role in solving many body problems in physics. The explicit construction of the Jack polynomials is an essential ingredient in solving the Calogero–Sutherland model, which is a one-dimensional integrable system. Starting from a special class of the Jack polynomials associated to the hook Young diagram, we find a systematic way in the explicit construction of the transition coefficients in the power-sum basis, which is closely related to a set of mutually commuting operators, i.e. the conserved charges.展开更多
The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work...The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.展开更多
We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c < ∞. We analyze the triangular structure hidde...We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c < ∞. We analyze the triangular structure hidden in the AGT relation with WNsymmetry in detail and the triangular structure implies the integrability.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.11035008
文摘Integrability plays a central role in solving many body problems in physics. The explicit construction of the Jack polynomials is an essential ingredient in solving the Calogero–Sutherland model, which is a one-dimensional integrable system. Starting from a special class of the Jack polynomials associated to the hook Young diagram, we find a systematic way in the explicit construction of the transition coefficients in the power-sum basis, which is closely related to a set of mutually commuting operators, i.e. the conserved charges.
基金Supported by the Chinese Academy of Sciences Program "Frontier Topics in Mathematical Physics" (KJCX3-SYW-S03)Supported Partially by the National Natural Science Foundation of China under Grant No.11035008
文摘The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
基金Supported by the Chinese Academy of S Sciences program"Frontier Topics in Mathematical Physics"(KJCX3-SYW-S03)by National Natural Science Foundation of China under Grant No.11035008
文摘We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c < ∞. We analyze the triangular structure hidden in the AGT relation with WNsymmetry in detail and the triangular structure implies the integrability.
