Please try this query:
1)
select ps.Name AS PartitionScheme, pf.name AS PartitionFunction,fg.name AS FileGroupName
from sys.indexes i
JOIN sys.partitions p ON i.object_id=p.object_id AND i.index_id=p.index_id
join sys.partition_schemes ps on ps.data_space_id = i.data_space_id
join sys.partition_functions pf on pf.function_id = ps.function_id
join sys.allocation_units au ON au.container_id = p.hobt_id
join sys.filegroups fg ON fg.data_space_id = au.data_space_id
where i.object_id = object_id('TableName')
or for more detailed information use the below query( SQL 2008 Internals Book)
2)
SELECT
ISNULL(quotename(ix.name),'Heap') as IndexName
,ix.type_desc as type
,prt.partition_number
,prt.data_compression_desc
,ps.name as PartitionScheme
,pf.name as PartitionFunction
,fg.name as FilegroupName
,case when ix.index_id < 2 then prt.rows else 0 END as Rows
,au.TotalMB
,au.UsedMB
,case when pf.boundary_value_on_right = 1 then 'less than' when pf.boundary_value_on_right is null then '' else 'less than or equal to' End as Comparison
,fg.name as FileGroup
,rv.value
FROM sys.partitions prt
inner join sys.indexes ix
on ix.object_id = prt.object_id and
ix.index_id = prt.index_id
inner join sys.data_spaces ds
on ds.data_space_id = ix.data_space_id
left join sys.partition_schemes ps
on ps.data_space_id = ix.data_space_id
left join sys.partition_functions pf
on pf.function_id = ps.function_id
left join sys.partition_range_values rv
on rv.function_id = pf.function_id AND
rv.boundary_id = prt.partition_number
left join sys.destination_data_spaces dds
on dds.partition_scheme_id = ps.data_space_id AND
dds.destination_id = prt.partition_number
left join sys.filegroups fg
on fg.data_space_id = ISNULL(dds.data_space_id,ix.data_space_id)
inner join (select str(sum(total_pages)*8./1024,10,2) as [TotalMB]
,str(sum(used_pages)*8./1024,10,2) as [UsedMB]
,container_id
from sys.allocation_units
group by container_id) au
on au.container_id = prt.partition_id
WHERE prt.OBJECT_ID = object_id(N'dbo.test')
order by ix.type_desc;