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<div dir="ltr"><div style="color:rgb(49,49,49);word-spacing:1px">As part of the series of seminars <i>"Insalate di Matematica"</i>, <b>Alice Dell'Arciprete</b>, PhD student at <span style="color:rgb(34,34,34);word-spacing:0px">the University of East Anglia</span><font style="word-spacing:0px" color="#313131"><span style="word-spacing:1px">, will deliver a talk. </span></font></div><div style="color:rgb(49,49,49);word-spacing:1px">The seminar will be held online and, according to the current Covid regulations, it <span>will also be broadcast in room 3014</span> <b>(more information below)</b>.</div><div style="color:rgb(49,49,49);word-spacing:1px"><br></div><div style="color:rgb(49,49,49);word-spacing:1px"><span style="color:rgb(34,34,34)">Here the details:</span></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><u>Date and time</u>: <b>18th November 2021, 2:00 pm </b></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><u>Title</u>: <i><span style="background-color:rgb(241,194,50)">"<span style="color:rgb(34,34,34)">Blocks of Ariki-Koike algebras"</span></span><br><span style="color:rgb(34,34,34);background-color:rgb(241,194,50)"></span></i></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="ltr"><u style="color:rgb(49,49,49);word-spacing:1px">Abstract</u><font color="#313131"><span style="word-spacing:1px">: </span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">R</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">epresentations
of the symmetric group are </span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">quite well understood, mainly thanks to a
</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">constructive approach given by James who developed the use of combinatorial tools,
such as diagrams, tableaux and abacuses. This approach </span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">can be
</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">generalise</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">d</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">
to give techniques for studying representations of related algebras
including the Hecke algebras of type A and the Ariki-Koike algebras. </span></font></div><div dir="ltr"><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">We consider representations of the Ariki–Koike algebra,
a q-deformation of the group algebra of the complex reflection group </span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal"><img alt="C_r" title="C_r" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=C%5Fr" id="m_4127686596674042823m_3689064146013177129l0.42027058043463406" style="display:inline;vertical-align:-2.667px" width="16" height="14"> </span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">wr <img alt="S_n" title="S_n" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=S%5Fn" id="m_4127686596674042823m_3689064146013177129l0.9799850952955675" style="display:inline;vertical-align:-2.667px" width="16" height="14"></span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">. The representations of th</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">is</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">
algebra are naturally indexed by mu</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">l</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal">tipartitions
of <img alt="n" title="n" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=n" id="m_4127686596674042823m_3689064146013177129l0.5340999640569375" style="display:inline" width="8" height="7">. We examine blocks of the Ariki–Koike algebra, in an attempt to
generalise the combinatorial representation theory of the Iwahori–Hecke
algebra.</span></font><font style="font-family:arial,sans-serif" size="2"><span style="line-height:normal"><br></span></font><span style="font-family:arial,sans-serif"><font size="2"></font></span><span style="font-family:arial,sans-serif"><font size="2"><span style="line-height:normal">In
particular, we prove a sufficient condition such
that restriction of modules leads to a natural correspondence between
the multipartitions of <img alt="n" title="n" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=n" id="m_4127686596674042823m_3689064146013177129l0.7442559658127477" style="display:inline" width="8" height="7"> whose Specht modules belong to a block <img alt="B" title="B" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=B" id="m_4127686596674042823m_3689064146013177129l0.6436856065165231" style="display:inline;vertical-align:-0.667px" width="11" height="11"> and
those of <img alt="n-\delta_i(B)" title="n-\delta_i(B)" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=n-%5Cdelta%5Fi(B)" id="m_4127686596674042823m_3689064146013177129l0.38504445277507826" style="display:inline;vertical-align:-4px" width="65" height="16"> </span></font><font size="2"><span style="line-height:normal"> whose Specht modules belong to the block <img alt="B'" title="B'" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=B'" id="m_4127686596674042823m_3689064146013177129l0.7401504914824946" style="display:inline;vertical-align:-0.333px" width="15" height="12"> </span><span style="line-height:normal">,
obtained from <img alt="B" title="B" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=B" id="m_4127686596674042823m_3689064146013177129l0.16545871022456993" style="display:inline;vertical-align:-0.667px" width="11" height="11"> applying a Scopes equivalence.</span></font></span><span style="font-family:arial,sans-serif"></span>
<div dir="auto"><u style="color:rgb(49,49,49);word-spacing:1px"><br>Keywords</u><font color="#313131"><span style="word-spacing:1px">: symmetric group, Ariki-Koike algebra, representation theory, combinatorics, abacus, block.
</span></font></div><div dir="auto"><br></div><div dir="auto" style="word-spacing:1px"><font color="#313131"><br></font></div><div style="word-spacing:1px"><font color="#313131"><b><u>Information to attend in room 3014<br></u></b></font></div><div style="word-spacing:1px"><font color="#313131">The
seminar will<span> also be broadcast</span>
in room 3014, at the building U5-Ratio,
Università degli Studi di Milano Bicocca. <span>For the traceability of persons present in the department</span>,
<span></span>
</font><span style="color:rgb(49,49,49)"> reservation is mandatory. You can reserve at the following link: </span><a href="https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0" target="_blank">https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0</a></div><div style="word-spacing:1px"><font color="#313131">We also remind that you will be required to exhibit your green pass at the entrance of the building.</font></div><div style="word-spacing:1px"><font color="#313131"><br></font></div><div style="word-spacing:1px"><b style="color:rgb(49,49,49)"><u>Information to attend online</u></b></div><div style="word-spacing:1px"><font color="#313131">The seminar will be streamed via</font><font color="#313131"> Google Meet platform at the following link: <a href="https://meet.google.com/jcy-vdby-bwn" target="_blank">https://meet.google.com/jcy-vdby-bwn</a><br></font><span style="font-family:Roboto,Arial,sans-serif;letter-spacing:0.3px;white-space:nowrap"></span></div><div dir="auto"><i><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk <u>after the starting time</u>, we kindly ask you to ensure that <u>your microphone and webcam are turned off</u> **</b></i><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px">You can find the poster of the event in the attachment. We are looking forward to seeing you!</div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br></div><div dir="auto" style="color:rgb(49,49,49);word-spacing:1px"><br>The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</div></div></div>
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