REVIEW 6 cited by
Affine Screening Operators, Affine Laumon Spaces, and Conjectures Concerning Non-Stationary Ruijsenaars Functions
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
Based on the screened vertex operators associated with the affine screening operators, we introduce the formal power series f^{hat{gl}_N}(x,p|s,kappa|q,t) which we call the non-stationary Ruijsenaars function. We identify it with the generating function for the Euler characteristics of the affine Laumon spaces. When the parameters s and kappa are suitably chosen, the limit t rightarrow q of f^{hat{gl}_N}(x,p|s,kappa|q,q/t) gives us the dominant integrable characters of hat{sl}_N multiplied by 1/(p^N;p^N)_infty (i.e. the hat{gl}_1 character). Several conjectures are presented for f^{hat{gl}_N}(x,p|s,kappa|q,t), including the bispectral and the Poincare dualities, and the evaluation formula. Main Conjecture asserts that (i) one can normalize f^{hat{gl}_N}(x,p|s,kappa|q,t) in such a way that the limit kappa rightarrow 1 exists, and (ii) the limit f^{st.hat{gl}_N}(x,p|s|q,t) gives us the eigenfunction of the elliptic Ruijsenaars operator. The non-stationary affine q-difference Toda operator T^{hat{gl}_N}(kappa) is introduced, which comes as an outcome of the study of the Poincare duality conjecture in the affine Toda limit t rightarrow 0. Main Conjecture is examined also in the limiting cases of the affine q-difference Toda (t rightarrow 0), and the elliptic Calogero-Sutherland (q,t rightarrow 1) equations.
Forward citations
Cited by 6 Pith papers
-
Spiralling branes, affine qq-characters and elliptic integrable systems
Quantum toroidal algebra intertwiners reproduce Ruijsenaars-Schneider and Koroteev-Shakirov Hamiltonians, Shiraishi functions, and a new proof of the noncommutative Jacobi identity for affine qq-characters.
-
Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
Integral representations are constructed for solutions of the non-stationary elliptic Calogero-Sutherland equation, yielding elliptic analogues of Jack polynomials for non-integer coupling values.
-
Surface Defects in $A$-type Little String Theories
The authors give a combinatorial partition function for A-type little string theories with a full-type surface defect and argue that two NS-limit regularizations are both regular due to a recursive pole-cancellation identity.
-
A basic triad in Macdonald theory
At t=q^{-m}, the Noumi-Shiraishi series reproduces the Baker-Akhiezer function, completing a triad with the Macdonald polynomials.
-
Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$
Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting auto...
-
Elliptic triad
The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.
Discussion (0). Continue with ORCID to comment.