[qualiteam]

There is no template variable that could say whether it is the home page, or not.
However, doing this check is a somewhat easy task.

In your custom module/theme decorate \XLite\Controller\Customer\ACustomer class and add the following method:

    public function isHomePage()
    {
        return 'main' === $this->getTarget();
    }

Now you can use this in any storefront template as follows (any of the following will work):

1.

<div IF="isHomePage()">....your code goes there...</div>

2.

{if:isHomePage()}
....your code goes there...
{end:}