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<top_article>
<mrnumber>MR2177119</mrnumber>
<author>Masuda, Tetsu</author>
<author_utf8>Tetsu MASUDA</author_utf8>
<title>Special Polynomials Associated with the Noumi-Yamada System of Type $A_5^{(1)}$</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>48</volume>
<year>2005</year>
<page>231--246</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-2/48_231.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR2177119</mathsci_link>
<abstract>A determinant formula for algebraic solutions to the Noumi-Yamada system of type $A_5^{(1)}$ is presented. This expression is regarded as a special case of the universal characters. The entries of the determinant are given by the Laguerre polynomials. Degeneration to the rational solutions to the Painlev&#233; IV equation is discussed.</abstract>
<keywords>Noumi-Yamada system, Special polynomials, Universal characters.</keywords>
<subject>33E17, 33C45, 34M55.</subject>
<fesi_info>
  <FILE>48-231</FILE>
  <YEAR>2005</YEAR>
  <TITLE>Special Polynomials Associated with the Noumi-Yamada System of Type $A_5^{(1)}$</TITLE>
  <AUTHOR>MASUDA, Tetsu</AUTHOR>
  <AUTHOR_utf8>Tetsu MASUDA</AUTHOR_utf8>
</fesi_info>

<references>

  <article>
<bibitem>1</bibitem>
<author>Kajiwara, K.; Ohta, Y.</author>
<title>Determinant structure of the rational solutions for the Painlev&#233; IV equation</title>
<journal>J. Phys. A: Math. Gen.</journal>
<vol>31</vol>
<year>1998</year>
<page>2431-2446</page>
<mr>MR1629434</mr>
  </article>

  <article>
<bibitem>2</bibitem>
<author>Koike, K.</author>
<title>On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters</title>
<journal>Adv. Math.</journal>
<vol>74</vol>
<year>1989</year>
<page>57-86</page>
<mr>MR0991410</mr>
  </article>

  <article>
<bibitem>3</bibitem>
<author>Masuda, T.</author>
<title>On the rational solutions of $q$-Painlev&#233; V equation</title>
<journal>Nagoya Math. J.</journal>
<vol>169</vol>
<year>2003</year>
<page>119-143</page>
<mr>MR1962525</mr>
  </article>

  <fearticle>
<bibitem>4</bibitem>
<author>Masuda, T.</author>
<title>On a class of algebraic solutions to the Painlev&#233; VI equation, its determinant formula and coalescence cascade</title>
<journal>Funkcial. Ekvac.</journal>
<vol>46</vol>
<year>2003</year>
<page>121-171</page>
<mr>MR1996296</mr>
<feart>1996296</feart>
  </fearticle>

  <article>
<bibitem>5</bibitem>
<author>Masuda, T.; Ohta, Y.; Kajiwara, K.</author>
<title>A determinant formula for a class of rational solutions of Painlev&#233; V equation</title>
<journal>Nagoya Math. J.</journal>
<vol>168</vol>
<year>2002</year>
<page>1-25</page>
<mr>MR1942391</mr>
  </article>

  <book>
<bibitem>6</bibitem>
<author>Noumi, M.</author>
<booktitle>Painlev&#233; equations through symmetry</booktitle>
<publisher>Translations of Mathematical Monographs Vol. 223, American Mathematical Society</publisher>
<year>2004</year>
<mr>MR2044201</mr>
  </book>

  <fearticle>
<bibitem>7</bibitem>
<author>Noumi, M.; Yamada, Y.</author>
<title>Higher order Painlev&#233; equations of type $A_l^{(1)}$</title>
<journal>Funkcial. Ekvac.</journal>
<vol>41</vol>
<year>1998</year>
<page>483-503</page>
<mr>MR1676885</mr>
<feart>1676885</feart>
  </fearticle>

  <article>
<bibitem>8</bibitem>
<author>Noumi, M.; Yamada, Y.</author>
<title>Affine Weyl groups, discrete dynamical systems and Painlev&#233; equations</title>
<journal>Commun. Math. Phys.</journal>
<vol>199</vol>
<year>1998</year>
<page>281-295</page>
<mr>MR1666847</mr>
  </article>

  <article>
<bibitem>9</bibitem>
<author>Noumi, M.; Yamada, Y.</author>
<title>Symmetries in the fourth Painlev&#233; equation and Okamoto polynomials</title>
<journal>Nagoya Math. J.</journal>
<vol>153</vol>
<year>1999</year>
<page>53-86</page>
<mr>MR1684551</mr>
  </article>

  <article>
<bibitem>10</bibitem>
<author>Okamoto, K.</author>
<title>Studies on the Painlev&#233; equations III, second and fourth Painlev&#233; equations, $P_{II}$ and $P_{IV}$</title>
<journal>Math. Ann.</journal>
<vol>275</vol>
<year>1986</year>
<page>221-255</page>
<mr>MR0854008</mr>
  </article>

  <other>
<bibitem>11</bibitem>
<raw_data>Tsuda, T., Toda equation and special polynomials associated with the Garnier system, preprint</raw_data>
<mr>MR2263717</mr>
  </other>

  <article>
<bibitem>12</bibitem>
<author>Tsuda, T.</author>
<title>Universal characters and an extension of the KP hierarchy</title>
<journal>Comm. Math. Phys.</journal>
<vol>248</vol>
<year>2004</year>
<page>501-526</page>
<mr>MR2076919</mr>
  </article>


</references>
</top_article>
