서강대학교

초록/요약 도움말

The infinite affine Lie algebras of type ABCD, also called (gl) over cap(infinity), (o) over cap(infinity), and (sp) over cap(infinity), are equivalent to subalgebras of the quantum W1+infinity algebras. They have well-known representations on the Fock space of a Dirac fermion (A infinity), a Majorana fermion ((A) over cap (infinity) and (D) over cap (infinity)), or a symplectic boson ((C) over cap (infinity)). Explicit formulas for the action of the quantum W1+infinity subalgebras on the Fock states are proposed for each representation. These formulas are the equivalent of the vertical presentation of the quantum toroidal gl(1) algebra Fock representation. They provide an alternative to the fermionic and bosonic expressions of the horizontal presentation. Furthermore, these algebras are known to have a deep connection with symmetric polynomials. The action of the quantum W1+infinity generators leads to the derivation of Pieri-like rules and q-difference equations for these polynomials. In the specific case of (B) over cap (infinity), a q-difference equation is obtained for Q-Schur polynomials indexed by strict partitions.