BUG: PeriodIndex inconsistent deserialization with HDF5 - PyTables
- [x] I have checked that this issue has not already been reported.
There was a issue 5 years ago mentioned that `.to_hdf()` acts inconsistently across Python2 & 3 on `PeriodIndex` for fixed format
https://github.com/pandas-dev/pandas/issues/16781

- [x] I have confirmed this bug exists on the latest version of pandas.

- [x] (optional) I have confirmed this bug exists on the master branch of pandas.
The bug exists, but behavior is different - see next comment

---

I noticed that the deserialization of a pandas Series/DataFrame with `PeriodIndex` from HDF5 file is inconsistent when using PyTables format: The retrieved series/df  index will be converted to `Int64Index` instead of `PeriodIndex`: See code below for example

```python
import pandas as pd
store = pd.HDFStore('test.h5')
series = pd.Series(index=pd.date_range(start='2015-01', end='2016-01', freq='M'), data=0).to_period('M')
df = pd.DataFrame(index=pd.date_range(start='2015-01', end='2016-01', freq='M'), data=0, columns=['a']).to_period('M')
store.put('/a/a', series, format='table')
store.put('/a/b', df, format='table')
```

```python
store.select('/a/a')
```
Output:
```
540    0
541    0
542    0
543    0
544    0
545    0
546    0
547    0
548    0
549    0
550    0
551    0
dtype: int64
```
```python
store.select('/a/b').index
```
Output:
```
Int64Index([540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551], dtype='int64')
```
#### Problem description

Inconsistent output with HDF5 file & PyTables format 

#### Output of ``pd.show_versions()``

<details>


INSTALLED VERSIONS
------------------
commit           : 2cb96529396d93b46abab7bbc73a208e708c642e
python           : 3.9.1.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19041
machine          : AMD64
processor        : AMD64 Family 25 Model 33 Stepping 0, AuthenticAMD
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : English_United States.1252

pandas           : 1.2.4
numpy            : 1.20.2
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 20.3.1
setuptools       : 51.0.0.post20201207
Cython           : None
pytest           : 6.2.4
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : 1.4.3
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.0.1
IPython          : 7.24.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.2
numexpr          : 2.7.3
odfpy            : None
openpyxl         : 3.0.7
pandas_gbq       : None
pyarrow          : 4.0.1
pyxlsb           : None
s3fs             : None
scipy            : 1.6.3
sqlalchemy       : None
tables           : 3.6.1
tabulate         : None
xarray           : None
xlrd             : 2.0.1
xlwt             : None
numba            : None

</details>
