Wedge product symbol (exterior/alternating product)

Question

This question has a similar title, but my question is different.
I would like to denote the kth exterior power similar to this:

wedge is too small and bigwedge is not only too big but also centered in a strange way:

Also, I don't like using Lambda instead. I tried the relsize package, which provides the command mathlarger{}. This is the result:

As you see, the wedge is still too small and there is too much space between the wedge and the letter k.
Do you know a good solution?

chsk · Accepted Answer

You mention that a regular upper-case Lambda won't cut it, but you could use a sans-serif one. I took the liberty of adapting @egreg's answer to this question:
documentclass{article}
usepackage[math-style=ISO]{unicode-math}
defaultfontfeatures{Scale=MatchUppercase}
setmathfontfacemathsans{TeX Gyre Heros}
newcommand{wedgeprod}{mathsans{mupLambda}}
begin{document}
$$wedgeprod^k V = {} underbrace{ V wedge V dots wedge V }_{text{$k$ times}}$$
end{document}

This produces:

Definitely far from perfect, but better than nothing.

Sebastiano · Answer

Here I add my proposal using a newcommand bigw (of the standard symbol of Amsmath, bigwedge)  created with scalebox contained in graphicx package.
You can decrease the symbol bigw changing the parameter of scalebox{.95}[1].
documentclass[12pt]{article}
usepackage{amsmath,amssymb}
usepackage{graphicx}

newcommandbigw{scalebox{.95}[1]{$bigwedge$}}
begin{document}

[bigw^{!k}(V)=underbrace{V wedge V dotsb wedge V }_{k text{ times}}]

end{document}

Steven B. Segletes · Answer

Here I use a rotated text V to make the operator.  Based on the OP's figures, I employed sffamily.  Also, there appeared to be two sizes employed, so I mirrored that in lamop and lamopbold.
documentclass{article}
usepackage{amsmath,rotating}
DeclareMathOperatorlamopbold{rotatebox[origin=c]{180}{textsf{V}}}
DeclareMathOperatorlamop{rotatebox[origin=c]{180}{footnotesizetextsf{V}}}
begin{document}
[
 lamopbold^{!k}(V) = underbrace{V lamop dots lamop V}_{text{k times}}
]
end{document}

egreg · Answer

You can use a scaled down and raised up bigwedge symbol.
documentclass{article}
usepackage{amsmath}

makeatletter
newcommand{exterior}[1]{mathop{mathpaletteexterior@{#1}}}
newcommand{exterior@}[2]{%
  % raise to the baseline
  raisebox{depth}{%
  % select the script size relative to the current font
  fontsize{sf@size}{0}%
  % nullify the math surround
  m@th
  % typeset bigwedge, but using textstyle in displays
  $ifx#1displaystyletextstyleelse#1fibigwedge$}%
  % the exponent, a bit nearer to the symbol
  ^{mspace{-2mu}#2}%
  % remove the scriptspace
  kern-scriptspace
}
makeatother

begin{document}

begin{align}
exterior{k}V &= {underbrace{Vwedge Vwedgedotswedge V}_{text{$k$ times}}}

exterior{k}(V) &= {underbrace{Vwedge Vwedgedotswedge V}_{text{$k$ times}}}

a&=V_{exterior{k}V}
end{align}

end{document}

Wedge product symbol (exterior/alternating product)

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