arXiv subjects

Katsuhisa Mimachi

Publications and source records attributed to Katsuhisa Mimachi.

5 recordsLinked to original sources

arXiv2007

The connection problem associated with a Selberg type integral and the $q$-Racah polynomials

The connection problem associated with a Selberg type integral is solved. The connection coefficients are given in terms of the $q$-Racah polynomials. As an application of the explicit expression of the connection coefficients, examples of the monodromy-invariant Hermitian form of non-diagonal type are presented. It is noteworthy that such Hermitian forms are intimately related with the correlation functions of non-diagonal type in $\hat{sl_2}$-confromal field theory.

math-ph↗

arXiv2004

Regularizable cycles associated with a Selberg type integral under some resonance condition

We study the twisted homology group attached to a Selberg type integral under some resonance condition, which naturally appears in the su_2-conformal field theory and the representation of the Iwahori-Hecke algebra. We determine the dimension of the space of the regularizable cycles. The dimension-formula is given in terms of the generalized hypergeometric series.

math.AG↗

arXiv2002

Intersection numbers of twisted cycles and the correlation functions of the conformal field theory II

We evaluate the intersection numbers of loaded cycles and twisted forms associated with an n-fold Selberg-type integral. The result is deeply related with the geometry of the configuration space of n+3 points in the projective line.

math.AG↗

arXiv1997

Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_n$

We construct an integral representation of eigenfunctions for Macdonald's $q$-difference operator associated with the root system of type $C_n .$ It is given in terms of a restriction of a $q$-Jordan-Pochhammer integral. Choosing a suitable cycle of the integral, we obtain an integral representation of a special case of the Macdonald polynomial for the root system of type $C_n .$

q-alg↗

arXiv1996

A new derivation of the inner product formula for the Macdonald symmetric polynomials

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type $A_{n-1}$. As a special case, the corresponding constant term conjecture is also proved.

q-alg↗