Lattice equations arising from discrete Painlevé systems (I): $(A_2+A_1{)}^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$ cases

Abstract

We introduce the concept of $\omega$-lattice, constructed from $\tau$ functions of Painlevé systems, on which quad-equations of ABS type appear. In particular, we consider the $A_5^{(1)}$- and $A_6^{(1)}$-surface $q$-Painlevé systems corresponding affine Weyl group symmetries are of $(A_2+A_1{)}^{(1)}$- and $(A_1+A_1{)}^{(1)}$-types, respectively.

27 pages, 9 figure

References in corpus (4)

• q-Difference equations of KdV type and "Chazy-type" second-degree difference equations
• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• A geometric approach to tau-functions of difference Painlevé equations

Cited by in corpus (10)

• Cluster integrable systems, q-Painleve equations and their quantization
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• Geometric description of discrete power function associated with the sixth Painlevé equation
• Reduction of lattice equations to the Painlevé equations: P${}_{\mathrm{IV}}$ and P${}_{\mathrm{V}}$
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations