# Wedge Power symbol

I want the upper index to appear on slightly right and below the topmost part of wedge symbol. But $bigwedge^k V$ gives me the k at the top. How do I do this? I want this in the definition of exterior power of a vector space.

• Welcome to TeX.SE. It looks exactly like you describe. If you want to move it down further you can use $\bigwedge^{\raisebox{-0.4ex}{\scriptsize$k$}} V$. – Peter Grill Jun 29 '12 at 5:12
• This works properly in inline mode but when i use it inside  or \displaystyle , it does not work. How can i make it work in display mode. – DurgaDatta Jun 29 '12 at 5:15
• I just use \Lambda for exterior powers, reserving \bigwedge for the topological smash products. – Andrew Swann Apr 16 '13 at 6:22

If you don't like the default location in inline math, you can use \raisebox{<length>}{} to tweak the vertical position. To get the same behavior in display math use \nolimits:

## Code:

\documentclass{article}
\usepackage{graphicx}

\begin{document}
Inline math mode it works as $\bigwedge^{\raisebox{-0.4ex}{\scriptsize$k$}} V$.

In display math:
$\bigwedge\nolimits^k V$
\end{document}


\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\extp}{\@ifnextchar^\@extp{\@extp^{\,}}}
\def\@extp^#1{\mathop{\bigwedge\nolimits^{\!#1}}}
\makeatother

\begin{document}
displaystyle: $\displaystyle\extp^k V \otimes \frac{M}{N} \quad \extp Y$

\bigskip
inline style: $\extp^k V \quad \extp Y$

\bigskip
scriptstyle: $X_{\extp^k V}$

\bigskip
scriptscriptstyle: $X_{X_{\extp^k V}}$
\end{document}


With amsmath the cmex font scales properly in subscripts and superscripts.

• I'm not sure that qualifies as "simpler," but it's definitely more elegant. My one criticism (I can't really call it a "complaint" since I'm not the OP) is that in display style, the \extp symbol is still sized like a large operator. My own instincts (which may be mistaken) are that it should behave more like, e.g., \operatorname{Sym} (for symmetric product). In particular, not only the sub/superscript placement but also the character size in display style should imitate the inline version. – Charles Staats Apr 30 '13 at 0:04

The problem here is really that \bigwedge is apparently designed to be used as an abbreviation for "wedge a bunch of things together," much like the \sum and \prod symbols. An exterior power is a completely different animal in terms of spacing. While I don't really know what I'm doing here, I've made an attempt to create a macro \Exterior that gives a command with spacing and appearance appropriate for the exterior product:

\documentclass{article}

\newcommand{\Exterior}{\mathchoice{{\textstyle\bigwedge}}%
{{\bigwedge}}%
{{\textstyle\wedge}}%
{{\scriptstyle\wedge}}}

\begin{document}
displaystyle:
$\Exterior^k V \otimes \frac{M}{N}$

inline style: $\Exterior^k V$

\bigskip
scriptstyle: $X_{\Exterior^k V}$

\bigskip
scriptscriptstyle: $X_{X_{\Exterior^k V}}$
\end{document}


Output:

As you can see, it's not perfect, but I think it's closer to what we want for an exterior power. Perhaps someone more knowledgable can tweak the macro or rewrite it completely to produce a better result and/or make the code less of a hack.

I prefer this solution, I think it looks similar to what is used in, e.g., Hartshorne's Algebraic Geometry

\newcommand{\largewedge}{\mbox{\Large $\wedge$}}

• This does not scale with subscripts. – red_trumpet Mar 4 '19 at 9:15

Andrew Swann suggested in the comments to use \Lambda as an alternative to variations of \wedge or \bigwedge. This is what I currently do.

There are some shenanigans with fontspec and amsmath, but they can be resolved by using the unicode glyph Λ instead of \Lambda.

To obtain a style more similar to \wedge, use \mathsf{Λ} to use the the sans serif font.

Example code:

\documentclass{article}

\usepackage{fontspec}
\usepackage{amsmath}

\DeclareMathOperator{\Ext}{Λ}
\DeclareMathOperator{\Extalt}{\mathsf{Λ}}

\begin{document}

\begin{align*}
\Ext^k V \\
\Extalt^k V
\end{align*}

\end{document}


Output: