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Now that I read the linked issues I understand better the purpose of keeping all multi indexes (e.g. do not remove an index date), but having duplicate indexes without any warning is somewhat unexpected and could lead to bugs.
IMO having a parameter that could control this (like group_keys) would be very useful.
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Reproducible Example
Results in:

Issue Description
When applying a rolling operation on a dataframe grouped by a multi-index, the indexes are duplicated in the resulting dataframe.
Expected Behavior
The expected behavior is that the index is not duplicated.
This is the behavior when using apply instead of rolling directly, but this approach is slower compared to the first:
Results in:

Installed Versions
INSTALLED VERSIONS
commit : 8dab54d
python : 3.10.4.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.149-133.644.amzn2.x86_64
Version : #1 SMP Tue Oct 18 16:52:42 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8
pandas : 1.5.2
numpy : 1.23.2
pytz : 2022.2.1
dateutil : 2.8.2
setuptools : 65.6.3
pip : 22.3
Cython : 0.29.32
pytest : 7.1.2
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.9.1
html5lib : None
pymysql : None
psycopg2 : 2.9.3
jinja2 : 3.1.2
IPython : 8.4.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.5.3
numba : None
numexpr : None
odfpy : None
openpyxl : 3.0.10
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.9.1
snappy : None
sqlalchemy : 1.4.40
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None
tzdata : 2022.7
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