Matching Tag: vertex-operators
Let Φ ~ ( z ) : F u ⃗ → F v ⃗ \widetilde\Phi(z):\mathcal F_{\vec u}\to\mathcal F_{\vec v} Φ ( z ) : F u → F v be the crystal-limit vertex operator, with u ⃗ = ( u 1 , u 2 ) \vec u=(u_1,u_2) u = ( u 1 , u 2 ) and v ⃗ = ( v 1 , v 2 ) \vec v=(v_1,v_2) v = ( v 1 , v 2 ) , and let…
Let F F F be the set of the following 13 partitions: … Define … … For 1 ≤ a ≤ 3 1\leq a\leq3 1 ≤ a ≤ 3 , let L a \mathsf L_a L a be the set of partitions that do not begin with any c ∈ I a \boldsymbol c\in I_a c ∈ I a and…
Let Φ Λ , Λ Δ ( α , β , c ∅ ; z ) \Phi^{\Delta}_{\Lambda,\Lambda}(\alpha,\beta,c_{\emptyset};z) Φ Λ , Λ Δ ( α , β , c ∅ ; z ) be a ramified irregular vertex operator with expansion coefficients c λ ( m ) c_{\lambda}^{(m)} c λ ( m ) , and let…
Let p , q p,q p , q be positive integers, let … and let χ p , q \chi_{p,q} χ p , q be the singular vector of level p q pq pq in M Δ p , q M_{\Delta_{p,q}} M Δ p , q . A ramified irregular vertex operator is called singular when…
Let r r r be a positive integer and let M Λ [ r ] M^{[r]}_{\Lambda} M Λ [ r ] be an irregular Verma module with Λ 2 r − 1 ≠ 0 \Lambda_{2r-1}\neq 0 Λ 2 r − 1 = 0 and Λ 2 r = 0 \Lambda_{2r}=0 Λ 2 r = 0 . A ramified irregular vertex operator has an…
Let u = ( u 1 , … , u m ) \mathbf{u}=(u_1,\ldots,u_m) u = ( u 1 , … , u m ) and v = ( v 1 , … , v m ) \mathbf{v}=(v_1,\ldots,v_m) v = ( v 1 , … , v m ) , and let Φ ( w ) = Φ u v ( w ) : F u → F v \Phi(w)=\Phi_{\mathbf{u}}^{\mathbf{v}}(w):\mathcal{F}_{\mathbf{u}}\to\mathcal{F}_{\mathbf{v}} Φ ( w ) = Φ u v ( w ) : F u → F v be the…
Eigenvalue conjecture. The eigenvalues of [ η ( z ; p q − 1 t ) ] 1 \big[\eta(z;p q^{-1}t)\big]_1 [ η ( z ; p q − 1 t ) ] 1 on F \mathcal{F} F are given by