<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content="text/html; charset=iso-8859-1" http-equiv=Content-Type>
<META name=GENERATOR content="MSHTML 8.00.6001.19120">
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT size=2 face=Arial>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoTitle align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 18pt"><?xml:namespace
prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p><SPAN
style="TEXT-DECORATION: none"><STRONG><U></U></STRONG></SPAN></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoTitle align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 18pt"><STRONG><U>SEMINARIO
DI <SPAN style="mso-no-proof: yes">TEORIA DELLE
RAPPRESENTAZIONI</SPAN><o:p></o:p></U></STRONG></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoTitle align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt"><o:p><SPAN
style="TEXT-DECORATION: none"><STRONG><U></U></STRONG></SPAN></o:p></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"></SPAN> </H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">lunedì 5
settembre 2011</SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></H2>
<P
style="TEXT-ALIGN: center; LINE-HEIGHT: 18pt; MARGIN: 0cm 0cm 0pt 9pt; tab-stops: 324.0pt"
class=MsoNormal align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">ore <SPAN
style="mso-no-proof: yes">16.00</SPAN><o:p></o:p></SPAN></P>
<P
style="TEXT-ALIGN: center; LINE-HEIGHT: 18pt; MARGIN: 0cm 0cm 0pt 9pt; tab-stops: 324.0pt"
class=MsoNormal align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt"><o:p> </o:p></SPAN></P>
<P
style="TEXT-ALIGN: center; LINE-HEIGHT: 18pt; MARGIN: 0cm 0cm 0pt 9pt; tab-stops: 324.0pt"
class=MsoNormal align=center><U><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
<P
style="TEXT-ALIGN: center; LINE-HEIGHT: 18pt; MARGIN: 0cm 0cm 0pt 9pt; tab-stops: 324.0pt"
class=MsoNormal align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">Pisa<o:p></o:p></SPAN></P>
<P
style="TEXT-ALIGN: center; LINE-HEIGHT: 18pt; MARGIN: 0cm 0cm 0pt 9pt; tab-stops: 324.0pt"
class=MsoNormal align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">(Aula <SPAN
style="mso-no-proof: yes">Bianchi</SPAN>)<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt" class=MsoNormal><B><U><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt"><o:p><SPAN
style="TEXT-DECORATION: none"></SPAN></o:p></SPAN></U></B></P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt" class=MsoNormal
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 22pt; mso-ansi-language: EN-US; mso-no-proof: yes"
lang=EN-US></SPAN></I></B> </P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt" class=MsoNormal
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 22pt; mso-ansi-language: EN-US; mso-no-proof: yes"
lang=EN-US>Dmitri Panyushev<o:p></o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt" class=MsoNormal
align=center><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 11pt; mso-ansi-language: EN-US; mso-no-proof: yes"
lang=EN-US>Independent University of Moscow</SPAN></I><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 11pt; mso-ansi-language: EN-US"
lang=EN-US><o:p></o:p></SPAN></I></P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt" class=MsoNormal
align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"
lang=EN-US><o:p><FONT size=3> </FONT></o:p></SPAN></P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"
class=MsoNormal align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">Terrà un
seminario dal titolo:<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P style="TEXT-ALIGN: center; MARGIN: 0cm 0cm 0pt" class=MsoNormal
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 22pt; mso-ansi-language: EN-GB"
lang=EN-GB>“<SPAN style="mso-no-proof: yes">Fredman's reciprocity for invariants
of abelian groups and permanent of the Cayley
table</SPAN>”<o:p></o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p> </o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB>Abstract<o:p></o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p> </o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB; mso-no-proof: yes"
lang=EN-GB>Let R be the regular representation of a finite abelian group G and
let C_n denote the cyclic group of order n. For G=C_n, we compute the Poincare
series of all C_n-isotypic components in the symmetric tensor exterior algebra
of R. From this we derive a general reciprocity, which relates different cyclic
groups, and some number-theoretic identities. This generalises results of
Fredman and Elashvili--Jibladze. Then we consider the Cayley table, M_G, of G
and some generalisations of it. In particular, we prove that the number of
formally different terms in the permanent of M_G equals S^n(R)^G, where n is the
order of G.</SPAN></I><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p></o:p></SPAN></I></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p> </o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p> </o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB><o:p> </o:p></SPAN></I></B></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt">Tutti gli
interessati sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt"><o:p> </o:p></SPAN></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt"><o:p> </o:p></SPAN></P>
<P style="TEXT-ALIGN: justify; MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt"><o:p> </o:p></SPAN></P>
<P style="tab-stops: 9.0cm"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt; mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2">
</SPAN></SPAN><FONT face="Times New Roman"><SPAN
style="mso-ansi-language: IT"><SPAN style="mso-tab-count: 2"><FONT
size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 16pt; mso-ansi-language: IT">Classe
di Scienze<o:p></o:p></SPAN></FONT></P>
<P style="tab-stops: 9.0cm"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 8pt; mso-ansi-language: IT"><o:p> </o:p></SPAN></P></FONT></DIV>
<DIV><FONT size=2 face=Arial>- - - - -<BR>Michele VERDE<BR>Scuola Normale
Superiore<BR>Servizio Supporto Attività Didattiche<BR>Piazza Dei Cavalieri,
7<BR>I - 56126 Pisa</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>Tel. 050-509048<BR>Fax. 050-509045<BR>E-Mail: <A
href="mailto:michele.verde@sns.it">michele.verde@sns.it</A><BR>E-Mail: <A
href="mailto:adi.sd@sns.it">adi.sd@sns.it</A><BR>E-Mail: <A
href="mailto:didattica@sns.it">didattica@sns.it</A><BR>- - - - -</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>Le informazioni contenute nella presente e-mail e
nei relativi allegati possono essere riservate e sono, comunque, destinate
esclusivamente al destinatario in indirizzo.<BR>E’ vietata, pertanto, la
diffusione, distribuzione e/o copiatura di tali informazioni da parte di
qualsiasi soggetto diverso dal destinatario. <BR>Chiunque abbia ricevuto o letto
questa e-mail per errore o senza esserne legittimato è invitato a darne
immediatamente notizia al mittente tramite fax o e-mail e a
distruggerla.<BR>Grazie.<BR></FONT></DIV></BODY></HTML>