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lc ICERM # at Brandan Jonathan page - oil Qcq ,t ) lk= Qcq ) - PowerPoint PPT Presentation

Oct 05, 2023 •267 likes •342 views

Talk lc ICERM # at Brandan Jonathan page - oil Qcq ,t ) lk= Qcq ) z=q maybe Work or over . braids plus stand Hecke combinations Hn= type A 1k their of n algebra fryy 7 . 5- g) ( stg ' ) :( -0 relation qeadwti . 65

  1. Talk lc ICERM # at Brandan Jonathan page - oil Qcq ,t ) lk= Qcq ) z=q maybe Work or over . braids plus stand Hecke combinations Hn= type A 1k their of n algebra fryy ¥7 . 5- g) ( stg ' ) :( -0 relation qeadwti . 65 } 2 , 4 # 5-51=-2 braid ! elation ' sysitsi of course -2 Tp If * = relation skein - : relation niolibk = gyn plus ¥ add generators Hecke f• affie Attn algebra - : X , Xn " ... Sn cater . ,Xn± ] Bernstein AH |k[X,± , ZCAH . ) - = , . T when RH edge X.tl on fo Hn = AH ... → , , Z ( Hn ) . Gahan ) ZCAHN ) ( Dipper Francis - Jones → Theorem ,

  2. Talk Zd Brandan ICERM # Jonathan at page removed } , Xn ) |× with fist a partition of { m×( Xii column Basis for n ZCHN ) = . . : . XP monomial XP ! symmetric polynomial " Hsym ) . ¥ his T eg * # rreps ZCHN ) = # partitions of dim Size n = = X ,tXztXztX4tXs n?okaan±= X±n ± CXF %-) maps ) The ZCHN ) Sym her Corollary e. ... , , , 7 Symmettifuctwi ODT "→ , asymptotically faithful are @ Sym ¥045 ZCHN ) to asymptotically faithful is Sym . The Conjecture map Sage ? XY . ?s X into to convert Difficult computationally . . . why ? ? Rest of the talk :

  3. k= -2 Talk 3f Brandan ICERM # at Jonathan page k€27 central Heisnft ,t ) charge Heisenberg category c- : Declare f) ( khouanou ) Idea lk hniarstnifmonoidal category . h= Heisenberg Liedgebn = identity adomorphusin T , f , Monoidal of V Objects ^ , Pn , qn c ^o^@u=^^v presentation " ' , ,9i+2=EiP :vz•=¥HcYded£a skein relation % I Baidelakon fmmc Morpwsin [ pn ,qm|= , , , .tn?nsT.trYUiiJ=ytz...Ag ccertol A V Adjuidins , afpieteekealatroi ^ Invertible , µ=T=4 Seek monoidal category i=Vf * Let . =~ Ufhy so P forces , k° T Case <c=k V . ] > Gmthudiecknig 17 V invertible is v ] q ,=[ K p ,=[^ ] - - t , data One more , ]=k [ p , ,q ! AND SO On

  4. Brandan Talk ICERM 4c Jonathan # at page ... Heiskk , t ) ? bases for moplusin ' Basic question in spaces now ( 11 ) Bubbles End v v • • . . . na eg 27 % ~ conjecture ! Follows from earlier 's .dz Sym @ fgm .tt C , " " it ) Hn induction Heis mod T acts nztf The point by . : . " restrictor " f by acts level Zcydobmi Hecke algebras G An with ,t ) replace Her : o easier k=O slightly ! I 'll show the To finish case - you , ) ( Turaev Is affinitaton of HOMFLY Heisofz ,t ) skein category In fact ,

  5. Brandan Jonathan Talk 5b ICERM # at page DIDIIIDI ' t=qn Dim Let . Uqlgen ) ftp.fng.l?ytI...ntEifit2l Quantum long ) group ' Erjfir - I Eirfrj Ej= { fg= higher " " 4 v VxoV@M-sVxoVxOM.R-matmVxoVD.v not qtfirfrj V natural representation Fir frj - ellneub dimension of m * f V Vxo acts @ T acts as - Heigcz .tl as - ffunctor ) % acts D as ( transformation ) natural . matrix squared R Vxom . Mxov M V @ UqGln ) - mod , acts → , as 12 = t.tt " ✓ n ) [ dimension Quantum 9q÷i of = = v ,

  6. Brandan Talk .9!H ICERM 6 b Jonathan # at page . , .mµl=Z( Uqfsen ) ) ,€k[xF , xntysn End ( Ida , ... Ennis → .ge ) ' E ( " Ei ,i= Fin Er ,iDr Frj Dj = =EM§" . X ; ' Xim Xiii § Xii i E , fin " ' " . , If it 0 m > v m • , ,§⇐t±¥" Eitiiiimfmgmosafetfeifsymmeni , ¥ Laurent sgmmeki functions ' . but I Similar ' place x. of If in . . meo The theorem basis follows THEIR °o°

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