Type Construction and Cycle Detection

Integral of a certain multivalued form over cycle $\pmbΔ$ provides zonal spherical function of type $A_n$. This paper is devoted to quantum group analysis and verification of monodromy properties of the distinguished cycle $\pmbΔ$. Zonal spherical function is a particular conformal block of $WA_n$-algebra.

In this paper, we introduce a Ketonen-type Gentzen-style classical simple type theory $\bf KCT$. Also the tableau system $\bf KCTT$ corresponding to $\bf KCT$ is introduced. Further inference-preserving Gentzen system $\bf KCT_h$ (equivalent to $\bf KCT$) and tableau system $\bf KCTT_h$ (equivalent to $\bf KCTT$) is introduced. We introduce the notion of Hintikka sequents for $\bf KCTT_h$.The completeness theorem and Takahashi-Prawitz's theorem are proved for $\bf KCTT_h$.