Institute of Mathematics for Industry

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Rigidity index and middle convolution of q-difference equations


Hold Date 2011-05-23 15:30~2011-05-23 17:00

Place Lecture Room S-1, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Masahito YAMAGUCHI (Tokyo University)

summary:
We consider $q$-difference system $E_R:Y(qx)=R(x)Y(x)$ with rational
function in element matrix coefficient.
At first we define spectral type and rigidity index of $E_R$. Next we
obtain classification of 2nd order irreducible rigid equations rigidity
index.
Moreover we define $q$-middle convolution algebraically. We can
recompose that as  analytical transformation using Euler transformation.
Finally we consider about the important properties that $q$-middle
convolution satisfies.