documentclass{article}
usepackage{amsmath,xparse}

DeclareMathOperator{TL}{T}

ExplSyntaxOn
NewDocumentCommand{Tgennew}{m m}
{TLleft[begin{smallmatrix} Tgennew_print:n {#1} \ Tgennew_print:n {#2} end{smallmatrix}right]
}

seq_new:N l_Tgennew_list_seq
tl_new:N l_Tgennew_last_tl
cs_new_protected:Npn Tgennew_print:n #1
{
  seq_set_split:Nnn l_Tgennew_list_seq { , } { #1 }
  seq_pop_right:NN l_Tgennew_list_seq l_Tgennew_last_tl
  seq_map_inline:Nn l_Tgennew_list_seq { ##1 , &  }
  tl_use:N l_Tgennew_last_tl
}
ExplSyntaxOff


begin{document}
$Tgennew{111,2,3333,4,5}{a,b,c,d,eee}$

or, with a couple of variables:

$Tgennew{alpha_1, alpha_2, dots, alpha_ell}{beta_1, beta_2, dots, beta_ell}$
end{document}